id	sid	tid	token	lemma	pos
ejpam-5494	1	1	european	european	PROPN
ejpam-5494	1	2	journal	journal	PROPN
ejpam-5494	1	3	of	of	ADP
ejpam-5494	1	4	pure	pure	ADJ
ejpam-5494	1	5	and	and	CCONJ
ejpam-5494	1	6	applied	apply	VERB
ejpam-5494	1	7	mathematics	mathematic	NOUN
ejpam-5494	1	8	vol	vol	NOUN
ejpam-5494	1	9	.	.	PROPN
ejpam-5494	2	1	17	17	NUM
ejpam-5494	2	2	,	,	PUNCT
ejpam-5494	2	3	no	no	INTJ
ejpam-5494	2	4	.	.	NOUN
ejpam-5494	2	5	4	4	NUM
ejpam-5494	2	6	,	,	PUNCT
ejpam-5494	2	7	2024	2024	NUM
ejpam-5494	2	8	,	,	PUNCT
ejpam-5494	2	9	3826	3826	NUM
ejpam-5494	2	10	-	-	SYM
ejpam-5494	2	11	3846	3846	NUM
ejpam-5494	2	12	issn	issn	PROPN
ejpam-5494	2	13	1307	1307	NUM
ejpam-5494	2	14	-	-	SYM
ejpam-5494	2	15	5543	5543	NUM
ejpam-5494	2	16	–	–	PUNCT
ejpam-5494	2	17	ejpam.com	ejpam.com	X
ejpam-5494	2	18	published	publish	VERB
ejpam-5494	2	19	by	by	ADP
ejpam-5494	2	20	new	new	PROPN
ejpam-5494	2	21	york	york	PROPN
ejpam-5494	2	22	business	business	PROPN
ejpam-5494	2	23	global	global	ADJ
ejpam-5494	2	24	employing	employ	VERB
ejpam-5494	2	25	the	the	DET
ejpam-5494	2	26	sadik	sadik	PROPN
ejpam-5494	2	27	residual	residual	ADJ
ejpam-5494	2	28	power	power	NOUN
ejpam-5494	2	29	series	series	PROPN
ejpam-5494	2	30	method	method	NOUN
ejpam-5494	2	31	to	to	PART
ejpam-5494	2	32	analyze	analyze	VERB
ejpam-5494	2	33	a	a	DET
ejpam-5494	2	34	system	system	NOUN
ejpam-5494	2	35	of	of	ADP
ejpam-5494	2	36	nonlinear	nonlinear	PROPN
ejpam-5494	2	37	caputo	caputo	PROPN
ejpam-5494	2	38	time	time	PROPN
ejpam-5494	2	39	-	-	PUNCT
ejpam-5494	2	40	fractional	fractional	ADJ
ejpam-5494	2	41	partial	partial	ADJ
ejpam-5494	2	42	differential	differential	NOUN
ejpam-5494	2	43	equations	equation	NOUN
ejpam-5494	2	44	prapart	prapart	VERB
ejpam-5494	2	45	pue	pue	NOUN
ejpam-5494	2	46	-	-	PUNCT
ejpam-5494	2	47	on	on	ADP
ejpam-5494	2	48	mathematics	mathematic	NOUN
ejpam-5494	2	49	and	and	CCONJ
ejpam-5494	2	50	applied	apply	VERB
ejpam-5494	2	51	mathematics	mathematics	PROPN
ejpam-5494	2	52	research	research	NOUN
ejpam-5494	2	53	unit	unit	NOUN
ejpam-5494	2	54	,	,	PUNCT
ejpam-5494	2	55	department	department	NOUN
ejpam-5494	2	56	of	of	ADP
ejpam-5494	2	57	mathematics	mathematic	NOUN
ejpam-5494	2	58	,	,	PUNCT
ejpam-5494	2	59	faculty	faculty	NOUN
ejpam-5494	2	60	of	of	ADP
ejpam-5494	2	61	science	science	NOUN
ejpam-5494	2	62	,	,	PUNCT
ejpam-5494	2	63	mahasarakham	mahasarakham	PROPN
ejpam-5494	2	64	university	university	PROPN
ejpam-5494	2	65	,	,	PUNCT
ejpam-5494	2	66	maha	maha	PROPN
ejpam-5494	2	67	sarakham	sarakham	PROPN
ejpam-5494	2	68	,	,	PUNCT
ejpam-5494	2	69	44150,thailand	44150,thailand	PROPN
ejpam-5494	2	70	abstract	abstract	NOUN
ejpam-5494	2	71	.	.	PUNCT
ejpam-5494	3	1	the	the	DET
ejpam-5494	3	2	present	present	ADJ
ejpam-5494	3	3	study	study	NOUN
ejpam-5494	3	4	proposes	propose	VERB
ejpam-5494	3	5	an	an	DET
ejpam-5494	3	6	approximate	approximate	ADJ
ejpam-5494	3	7	analytical	analytical	ADJ
ejpam-5494	3	8	solution	solution	NOUN
ejpam-5494	3	9	to	to	ADP
ejpam-5494	3	10	a	a	DET
ejpam-5494	3	11	nonlinear	nonlinear	ADJ
ejpam-5494	3	12	system	system	NOUN
ejpam-5494	3	13	of	of	ADP
ejpam-5494	3	14	time	time	NOUN
ejpam-5494	3	15	-	-	PUNCT
ejpam-5494	3	16	fractional	fractional	ADJ
ejpam-5494	3	17	partial	partial	ADJ
ejpam-5494	3	18	differential	differential	NOUN
ejpam-5494	3	19	equations	equation	NOUN
ejpam-5494	3	20	.	.	PUNCT
ejpam-5494	4	1	the	the	DET
ejpam-5494	4	2	sadik	sadik	PROPN
ejpam-5494	4	3	residual	residual	ADJ
ejpam-5494	4	4	power	power	NOUN
ejpam-5494	4	5	series	series	NOUN
ejpam-5494	4	6	method	method	NOUN
ejpam-5494	4	7	,	,	PUNCT
ejpam-5494	4	8	which	which	PRON
ejpam-5494	4	9	integrates	integrate	VERB
ejpam-5494	4	10	the	the	DET
ejpam-5494	4	11	two	two	NUM
ejpam-5494	4	12	-	-	PUNCT
ejpam-5494	4	13	part	part	NOUN
ejpam-5494	4	14	sadik	sadik	ADJ
ejpam-5494	4	15	integral	integral	ADJ
ejpam-5494	4	16	transform	transform	NOUN
ejpam-5494	4	17	with	with	ADP
ejpam-5494	4	18	the	the	DET
ejpam-5494	4	19	residual	residual	ADJ
ejpam-5494	4	20	power	power	NOUN
ejpam-5494	4	21	series	series	NOUN
ejpam-5494	4	22	technique	technique	NOUN
ejpam-5494	4	23	,	,	PUNCT
ejpam-5494	4	24	is	be	AUX
ejpam-5494	4	25	employed	employ	VERB
ejpam-5494	4	26	to	to	PART
ejpam-5494	4	27	solve	solve	VERB
ejpam-5494	4	28	the	the	DET
ejpam-5494	4	29	fractional	fractional	ADJ
ejpam-5494	4	30	differential	differential	ADJ
ejpam-5494	4	31	equation	equation	NOUN
ejpam-5494	4	32	in	in	ADP
ejpam-5494	4	33	the	the	DET
ejpam-5494	4	34	caputo	caputo	PROPN
ejpam-5494	4	35	sense	sense	NOUN
ejpam-5494	4	36	.	.	PUNCT
ejpam-5494	5	1	nonlinear	nonlinear	ADJ
ejpam-5494	5	2	problems	problem	NOUN
ejpam-5494	5	3	with	with	ADP
ejpam-5494	5	4	known	known	ADJ
ejpam-5494	5	5	and	and	CCONJ
ejpam-5494	5	6	unknown	unknown	ADJ
ejpam-5494	5	7	solutions	solution	NOUN
ejpam-5494	5	8	are	be	AUX
ejpam-5494	5	9	examined	examine	VERB
ejpam-5494	5	10	to	to	PART
ejpam-5494	5	11	demonstrate	demonstrate	VERB
ejpam-5494	5	12	the	the	DET
ejpam-5494	5	13	capacity	capacity	NOUN
ejpam-5494	5	14	of	of	ADP
ejpam-5494	5	15	the	the	DET
ejpam-5494	5	16	technique	technique	NOUN
ejpam-5494	5	17	.	.	PUNCT
ejpam-5494	6	1	numerical	numerical	ADJ
ejpam-5494	6	2	simulations	simulation	NOUN
ejpam-5494	6	3	and	and	CCONJ
ejpam-5494	6	4	3d	3d	NUM
ejpam-5494	6	5	visualizations	visualization	NOUN
ejpam-5494	6	6	are	be	AUX
ejpam-5494	6	7	conducted	conduct	VERB
ejpam-5494	6	8	for	for	ADP
ejpam-5494	6	9	various	various	ADJ
ejpam-5494	6	10	values	value	NOUN
ejpam-5494	6	11	of	of	ADP
ejpam-5494	6	12	the	the	DET
ejpam-5494	6	13	fractional	fractional	ADJ
ejpam-5494	6	14	order	order	NOUN
ejpam-5494	6	15	to	to	PART
ejpam-5494	6	16	further	far	ADV
ejpam-5494	6	17	understand	understand	VERB
ejpam-5494	6	18	the	the	DET
ejpam-5494	6	19	solution	solution	NOUN
ejpam-5494	6	20	’s	’s	PART
ejpam-5494	6	21	behavior	behavior	NOUN
ejpam-5494	6	22	.	.	PUNCT
ejpam-5494	7	1	additionally	additionally	ADV
ejpam-5494	7	2	,	,	PUNCT
ejpam-5494	7	3	the	the	DET
ejpam-5494	7	4	results	result	NOUN
ejpam-5494	7	5	are	be	AUX
ejpam-5494	7	6	validated	validate	VERB
ejpam-5494	7	7	against	against	ADP
ejpam-5494	7	8	exact	exact	ADJ
ejpam-5494	7	9	solutions	solution	NOUN
ejpam-5494	7	10	or	or	CCONJ
ejpam-5494	7	11	existing	exist	VERB
ejpam-5494	7	12	methodologies	methodology	NOUN
ejpam-5494	7	13	to	to	PART
ejpam-5494	7	14	ensure	ensure	VERB
ejpam-5494	7	15	their	their	PRON
ejpam-5494	7	16	reliability	reliability	NOUN
ejpam-5494	7	17	and	and	CCONJ
ejpam-5494	7	18	accuracy	accuracy	NOUN
ejpam-5494	7	19	.	.	PUNCT
ejpam-5494	8	1	a	a	DET
ejpam-5494	8	2	key	key	ADJ
ejpam-5494	8	3	advantage	advantage	NOUN
ejpam-5494	8	4	of	of	ADP
ejpam-5494	8	5	the	the	DET
ejpam-5494	8	6	proposed	propose	VERB
ejpam-5494	8	7	method	method	NOUN
ejpam-5494	8	8	is	be	AUX
ejpam-5494	8	9	its	its	PRON
ejpam-5494	8	10	ability	ability	NOUN
ejpam-5494	8	11	to	to	PART
ejpam-5494	8	12	generate	generate	VERB
ejpam-5494	8	13	results	result	NOUN
ejpam-5494	8	14	without	without	ADP
ejpam-5494	8	15	the	the	DET
ejpam-5494	8	16	need	need	NOUN
ejpam-5494	8	17	for	for	ADP
ejpam-5494	8	18	adomian	adomian	NOUN
ejpam-5494	8	19	polynomials	polynomial	NOUN
ejpam-5494	8	20	,	,	PUNCT
ejpam-5494	8	21	perturbation	perturbation	NOUN
ejpam-5494	8	22	techniques	technique	NOUN
ejpam-5494	8	23	,	,	PUNCT
ejpam-5494	8	24	discretization	discretization	NOUN
ejpam-5494	8	25	,	,	PUNCT
ejpam-5494	8	26	or	or	CCONJ
ejpam-5494	8	27	linearization	linearization	NOUN
ejpam-5494	8	28	,	,	PUNCT
ejpam-5494	8	29	enabling	enable	VERB
ejpam-5494	8	30	a	a	DET
ejpam-5494	8	31	more	more	ADV
ejpam-5494	8	32	efficient	efficient	ADJ
ejpam-5494	8	33	.	.	PUNCT
ejpam-5494	9	1	2020	2020	NUM
ejpam-5494	9	2	mathematics	mathematic	NOUN
ejpam-5494	9	3	subject	subject	NOUN
ejpam-5494	9	4	classifications	classification	NOUN
ejpam-5494	9	5	:	:	PUNCT
ejpam-5494	9	6	26a33	26a33	NUM
ejpam-5494	9	7	,	,	PUNCT
ejpam-5494	9	8	35r11	35r11	NUM
ejpam-5494	9	9	,	,	PUNCT
ejpam-5494	9	10	35a22	35a22	NUM
ejpam-5494	9	11	key	key	ADJ
ejpam-5494	9	12	words	word	NOUN
ejpam-5494	9	13	and	and	CCONJ
ejpam-5494	9	14	phrases	phrase	NOUN
ejpam-5494	9	15	:	:	PUNCT
ejpam-5494	9	16	residual	residual	ADJ
ejpam-5494	9	17	power	power	NOUN
ejpam-5494	9	18	series	series	NOUN
ejpam-5494	9	19	,	,	PUNCT
ejpam-5494	9	20	sadik	sadik	PROPN
ejpam-5494	9	21	transform	transform	PROPN
ejpam-5494	9	22	,	,	PUNCT
ejpam-5494	9	23	nonlinear	nonlinear	ADJ
ejpam-5494	9	24	system	system	NOUN
ejpam-5494	9	25	,	,	PUNCT
ejpam-5494	9	26	caputo	caputo	PROPN
ejpam-5494	9	27	fractional	fractional	ADJ
ejpam-5494	9	28	derivatives	derivative	NOUN
ejpam-5494	9	29	,	,	PUNCT
ejpam-5494	9	30	approximate	approximate	ADJ
ejpam-5494	9	31	solution	solution	NOUN
ejpam-5494	9	32	,	,	PUNCT
ejpam-5494	9	33	method	method	NOUN
ejpam-5494	9	34	1	1	NUM
ejpam-5494	9	35	.	.	PUNCT
ejpam-5494	9	36	introduction	introduction	NOUN
ejpam-5494	9	37	a	a	DET
ejpam-5494	9	38	fractional	fractional	ADJ
ejpam-5494	9	39	differential	differential	NOUN
ejpam-5494	9	40	equation	equation	NOUN
ejpam-5494	9	41	is	be	AUX
ejpam-5494	9	42	a	a	DET
ejpam-5494	9	43	generalization	generalization	NOUN
ejpam-5494	9	44	of	of	ADP
ejpam-5494	9	45	an	an	DET
ejpam-5494	9	46	integer	integer	NOUN
ejpam-5494	9	47	-	-	PUNCT
ejpam-5494	9	48	order	order	NOUN
ejpam-5494	9	49	differential	differential	ADJ
ejpam-5494	9	50	equation	equation	NOUN
ejpam-5494	9	51	that	that	PRON
ejpam-5494	9	52	appears	appear	VERB
ejpam-5494	9	53	in	in	ADP
ejpam-5494	9	54	various	various	ADJ
ejpam-5494	9	55	scientific	scientific	ADJ
ejpam-5494	9	56	frameworks	framework	NOUN
ejpam-5494	9	57	[	[	X
ejpam-5494	9	58	18	18	NUM
ejpam-5494	9	59	]	]	PUNCT
ejpam-5494	9	60	.	.	PUNCT
ejpam-5494	10	1	the	the	DET
ejpam-5494	10	2	study	study	NOUN
ejpam-5494	10	3	of	of	ADP
ejpam-5494	10	4	this	this	DET
ejpam-5494	10	5	sort	sort	NOUN
ejpam-5494	10	6	of	of	ADP
ejpam-5494	10	7	equation	equation	NOUN
ejpam-5494	10	8	has	have	AUX
ejpam-5494	10	9	gained	gain	VERB
ejpam-5494	10	10	increasing	increase	VERB
ejpam-5494	10	11	interest	interest	NOUN
ejpam-5494	10	12	among	among	ADP
ejpam-5494	10	13	scholars	scholar	NOUN
ejpam-5494	10	14	because	because	SCONJ
ejpam-5494	10	15	it	it	PRON
ejpam-5494	10	16	can	can	AUX
ejpam-5494	10	17	describe	describe	VERB
ejpam-5494	10	18	real	real	ADJ
ejpam-5494	10	19	-	-	PUNCT
ejpam-5494	10	20	world	world	NOUN
ejpam-5494	10	21	physical	physical	ADJ
ejpam-5494	10	22	phenomena	phenomenon	NOUN
ejpam-5494	10	23	in	in	ADP
ejpam-5494	10	24	greater	great	ADJ
ejpam-5494	10	25	detail	detail	NOUN
ejpam-5494	10	26	and	and	CCONJ
ejpam-5494	10	27	accuracy	accuracy	NOUN
ejpam-5494	10	28	than	than	SCONJ
ejpam-5494	10	29	integer	integer	NOUN
ejpam-5494	10	30	differential	differential	ADJ
ejpam-5494	10	31	equations	equation	NOUN
ejpam-5494	10	32	offer	offer	VERB
ejpam-5494	10	33	,	,	PUNCT
ejpam-5494	10	34	especially	especially	ADV
ejpam-5494	10	35	in	in	ADP
ejpam-5494	10	36	the	the	DET
ejpam-5494	10	37	physical	physical	ADJ
ejpam-5494	10	38	processes	process	NOUN
ejpam-5494	10	39	involving	involve	VERB
ejpam-5494	10	40	memory	memory	NOUN
ejpam-5494	10	41	and	and	CCONJ
ejpam-5494	10	42	heritability	heritability	NOUN
ejpam-5494	10	43	properties	property	NOUN
ejpam-5494	10	44	.	.	PUNCT
ejpam-5494	11	1	analyzing	analyze	VERB
ejpam-5494	11	2	non	non	ADJ
ejpam-5494	11	3	-	-	ADJ
ejpam-5494	11	4	linear	linear	ADJ
ejpam-5494	11	5	fractional	fractional	ADJ
ejpam-5494	11	6	differential	differential	NOUN
ejpam-5494	11	7	equations	equation	NOUN
ejpam-5494	11	8	has	have	AUX
ejpam-5494	11	9	become	become	VERB
ejpam-5494	11	10	an	an	DET
ejpam-5494	11	11	essential	essential	ADJ
ejpam-5494	11	12	challenge	challenge	NOUN
ejpam-5494	11	13	for	for	ADP
ejpam-5494	11	14	a	a	DET
ejpam-5494	11	15	century	century	NOUN
ejpam-5494	11	16	.	.	PUNCT
ejpam-5494	12	1	scientists	scientist	NOUN
ejpam-5494	12	2	have	have	AUX
ejpam-5494	12	3	attempted	attempt	VERB
ejpam-5494	12	4	to	to	PART
ejpam-5494	12	5	devise	devise	VERB
ejpam-5494	12	6	and	and	CCONJ
ejpam-5494	12	7	enhance	enhance	VERB
ejpam-5494	12	8	novel	novel	ADJ
ejpam-5494	12	9	approaches	approach	NOUN
ejpam-5494	12	10	,	,	PUNCT
ejpam-5494	12	11	whether	whether	SCONJ
ejpam-5494	12	12	analytical	analytical	ADJ
ejpam-5494	12	13	or	or	CCONJ
ejpam-5494	12	14	numerical	numerical	ADJ
ejpam-5494	12	15	,	,	PUNCT
ejpam-5494	12	16	for	for	ADP
ejpam-5494	12	17	conquering	conquer	VERB
ejpam-5494	12	18	such	such	ADJ
ejpam-5494	12	19	circumstances	circumstance	NOUN
ejpam-5494	12	20	.	.	PUNCT
ejpam-5494	13	1	among	among	ADP
ejpam-5494	13	2	these	these	DET
ejpam-5494	13	3	intriguing	intriguing	ADJ
ejpam-5494	13	4	methods	method	NOUN
ejpam-5494	13	5	are	be	AUX
ejpam-5494	13	6	the	the	DET
ejpam-5494	13	7	adomian	adomian	ADJ
ejpam-5494	13	8	decomposition	decomposition	NOUN
ejpam-5494	13	9	method	method	NOUN
ejpam-5494	13	10	[	[	X
ejpam-5494	13	11	15	15	NUM
ejpam-5494	13	12	]	]	PUNCT
ejpam-5494	13	13	,	,	PUNCT
ejpam-5494	13	14	[	[	X
ejpam-5494	13	15	24	24	NUM
ejpam-5494	13	16	]	]	PUNCT
ejpam-5494	13	17	,	,	PUNCT
ejpam-5494	13	18	[	[	X
ejpam-5494	13	19	30	30	NUM
ejpam-5494	13	20	]	]	PUNCT
ejpam-5494	13	21	,	,	PUNCT
ejpam-5494	13	22	homotopy	homotopy	NOUN
ejpam-5494	13	23	-	-	PUNCT
ejpam-5494	13	24	perturbation	perturbation	NOUN
ejpam-5494	13	25	method	method	NOUN
ejpam-5494	13	26	[	[	X
ejpam-5494	13	27	1	1	NUM
ejpam-5494	13	28	]	]	PUNCT
ejpam-5494	13	29	,	,	PUNCT
ejpam-5494	13	30	the	the	DET
ejpam-5494	13	31	homotopy	homotopy	NOUN
ejpam-5494	13	32	analysis	analysis	NOUN
ejpam-5494	13	33	method	method	NOUN
ejpam-5494	13	34	[	[	X
ejpam-5494	13	35	16	16	NUM
ejpam-5494	13	36	]	]	PUNCT
ejpam-5494	13	37	,	,	PUNCT
ejpam-5494	13	38	the	the	DET
ejpam-5494	13	39	differential	differential	ADJ
ejpam-5494	13	40	transform	transform	NOUN
ejpam-5494	13	41	method	method	NOUN
ejpam-5494	13	42	[	[	X
ejpam-5494	13	43	12	12	NUM
ejpam-5494	13	44	]	]	PUNCT
ejpam-5494	13	45	,	,	PUNCT
ejpam-5494	13	46	the	the	DET
ejpam-5494	13	47	chebyshev	chebyshev	PROPN
ejpam-5494	13	48	doi	doi	PROPN
ejpam-5494	13	49	:	:	PUNCT
ejpam-5494	13	50	https://doi.org/10.29020/nybg.ejpam.v17i4.5494	https://doi.org/10.29020/nybg.ejpam.v17i4.5494	PRON
ejpam-5494	13	51	email	email	NOUN
ejpam-5494	13	52	address	address	NOUN
ejpam-5494	13	53	:	:	PUNCT
ejpam-5494	13	54	prapart.p@msu.ac.th	prapart.p@msu.ac.th	PROPN
ejpam-5494	13	55	(	(	PUNCT
ejpam-5494	13	56	p.	p.	NOUN
ejpam-5494	13	57	pue	pue	NOUN
ejpam-5494	13	58	-	-	PUNCT
ejpam-5494	13	59	on	on	ADP
ejpam-5494	13	60	)	)	PUNCT
ejpam-5494	13	61	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5494	13	62	3826	3826	NUM
ejpam-5494	14	1	copyright	copyright	NOUN
ejpam-5494	14	2	:	:	PUNCT
ejpam-5494	14	3	©	©	PROPN
ejpam-5494	14	4	2024	2024	NUM
ejpam-5494	14	5	the	the	DET
ejpam-5494	14	6	author(s	author(s	NOUN
ejpam-5494	14	7	)	)	PUNCT
ejpam-5494	14	8	.	.	PUNCT
ejpam-5494	15	1	(	(	PUNCT
ejpam-5494	15	2	cc	cc	NOUN
ejpam-5494	15	3	by	by	ADP
ejpam-5494	15	4	-	-	PUNCT
ejpam-5494	15	5	nc	nc	PROPN
ejpam-5494	15	6	4.0	4.0	NUM
ejpam-5494	15	7	)	)	PUNCT
ejpam-5494	15	8	p.	p.	NOUN
ejpam-5494	15	9	pue	pue	NOUN
ejpam-5494	15	10	-	-	PUNCT
ejpam-5494	15	11	on	on	ADP
ejpam-5494	15	12	/	/	SYM
ejpam-5494	15	13	eur	eur	NOUN
ejpam-5494	15	14	.	.	PUNCT
ejpam-5494	16	1	j.	j.	PROPN
ejpam-5494	16	2	pure	pure	PROPN
ejpam-5494	16	3	appl	appl	PROPN
ejpam-5494	16	4	.	.	PROPN
ejpam-5494	16	5	math	math	PROPN
ejpam-5494	16	6	,	,	PUNCT
ejpam-5494	16	7	17	17	NUM
ejpam-5494	16	8	(	(	PUNCT
ejpam-5494	16	9	4	4	NUM
ejpam-5494	16	10	)	)	PUNCT
ejpam-5494	16	11	(	(	PUNCT
ejpam-5494	16	12	2024	2024	NUM
ejpam-5494	16	13	)	)	PUNCT
ejpam-5494	16	14	,	,	PUNCT
ejpam-5494	16	15	3826	3826	NUM
ejpam-5494	16	16	-	-	SYM
ejpam-5494	16	17	3846	3846	NUM
ejpam-5494	16	18	3827	3827	NUM
ejpam-5494	16	19	wavelets	wavelet	NOUN
ejpam-5494	16	20	method	method	NOUN
ejpam-5494	16	21	[	[	X
ejpam-5494	16	22	19	19	NUM
ejpam-5494	16	23	]	]	PUNCT
ejpam-5494	16	24	.	.	PUNCT
ejpam-5494	17	1	although	although	SCONJ
ejpam-5494	17	2	the	the	DET
ejpam-5494	17	3	procedures	procedure	NOUN
ejpam-5494	17	4	described	describe	VERB
ejpam-5494	17	5	above	above	ADV
ejpam-5494	17	6	are	be	AUX
ejpam-5494	17	7	reliable	reliable	ADJ
ejpam-5494	17	8	and	and	CCONJ
ejpam-5494	17	9	verifiable	verifiable	ADJ
ejpam-5494	17	10	,	,	PUNCT
ejpam-5494	17	11	they	they	PRON
ejpam-5494	17	12	come	come	VERB
ejpam-5494	17	13	with	with	ADP
ejpam-5494	17	14	practical	practical	ADJ
ejpam-5494	17	15	constraints	constraint	NOUN
ejpam-5494	17	16	and	and	CCONJ
ejpam-5494	17	17	require	require	VERB
ejpam-5494	17	18	a	a	DET
ejpam-5494	17	19	long	long	ADJ
ejpam-5494	17	20	time	time	NOUN
ejpam-5494	17	21	to	to	PART
ejpam-5494	17	22	generate	generate	VERB
ejpam-5494	17	23	results	result	NOUN
ejpam-5494	17	24	.	.	PUNCT
ejpam-5494	18	1	as	as	ADP
ejpam-5494	18	2	a	a	DET
ejpam-5494	18	3	result	result	NOUN
ejpam-5494	18	4	,	,	PUNCT
ejpam-5494	18	5	establishing	establish	VERB
ejpam-5494	18	6	a	a	DET
ejpam-5494	18	7	strategy	strategy	NOUN
ejpam-5494	18	8	for	for	ADP
ejpam-5494	18	9	effectively	effectively	ADV
ejpam-5494	18	10	addressing	address	VERB
ejpam-5494	18	11	issues	issue	NOUN
ejpam-5494	18	12	,	,	PUNCT
ejpam-5494	18	13	reducing	reduce	VERB
ejpam-5494	18	14	determining	determine	VERB
ejpam-5494	18	15	time	time	NOUN
ejpam-5494	18	16	,	,	PUNCT
ejpam-5494	18	17	and	and	CCONJ
ejpam-5494	18	18	making	make	VERB
ejpam-5494	18	19	it	it	PRON
ejpam-5494	18	20	advantageous	advantageous	ADJ
ejpam-5494	18	21	is	be	AUX
ejpam-5494	18	22	challenging	challenge	VERB
ejpam-5494	18	23	for	for	ADP
ejpam-5494	18	24	researchers	researcher	NOUN
ejpam-5494	18	25	.	.	PUNCT
ejpam-5494	19	1	sadik	sadik	PROPN
ejpam-5494	19	2	integral	integral	ADJ
ejpam-5494	19	3	transformation	transformation	NOUN
ejpam-5494	19	4	is	be	AUX
ejpam-5494	19	5	one	one	NUM
ejpam-5494	19	6	of	of	ADP
ejpam-5494	19	7	the	the	DET
ejpam-5494	19	8	most	most	ADV
ejpam-5494	19	9	vital	vital	ADJ
ejpam-5494	19	10	tools	tool	NOUN
ejpam-5494	19	11	used	use	VERB
ejpam-5494	19	12	to	to	PART
ejpam-5494	19	13	address	address	VERB
ejpam-5494	19	14	the	the	DET
ejpam-5494	19	15	issues	issue	NOUN
ejpam-5494	19	16	dealing	deal	VERB
ejpam-5494	19	17	with	with	ADP
ejpam-5494	19	18	fractional	fractional	ADJ
ejpam-5494	19	19	calculus	calculus	NOUN
ejpam-5494	19	20	in	in	ADP
ejpam-5494	19	21	science	science	NOUN
ejpam-5494	19	22	and	and	CCONJ
ejpam-5494	19	23	engineering	engineering	NOUN
ejpam-5494	19	24	[	[	X
ejpam-5494	19	25	25	25	NUM
ejpam-5494	19	26	]	]	PUNCT
ejpam-5494	19	27	,	,	PUNCT
ejpam-5494	19	28	[	[	X
ejpam-5494	19	29	28	28	NUM
ejpam-5494	19	30	]	]	PUNCT
ejpam-5494	19	31	,	,	PUNCT
ejpam-5494	19	32	[	[	X
ejpam-5494	19	33	26	26	NUM
ejpam-5494	19	34	]	]	PUNCT
ejpam-5494	19	35	.	.	PUNCT
ejpam-5494	20	1	the	the	DET
ejpam-5494	20	2	transform	transform	NOUN
ejpam-5494	20	3	is	be	AUX
ejpam-5494	20	4	considered	consider	VERB
ejpam-5494	20	5	to	to	PART
ejpam-5494	20	6	generalize	generalize	VERB
ejpam-5494	20	7	other	other	ADJ
ejpam-5494	20	8	important	important	ADJ
ejpam-5494	20	9	integral	integral	ADJ
ejpam-5494	20	10	transformations	transformation	NOUN
ejpam-5494	20	11	since	since	SCONJ
ejpam-5494	20	12	this	this	DET
ejpam-5494	20	13	transformation	transformation	NOUN
ejpam-5494	20	14	can	can	AUX
ejpam-5494	20	15	be	be	AUX
ejpam-5494	20	16	reduced	reduce	VERB
ejpam-5494	20	17	to	to	ADP
ejpam-5494	20	18	others	other	NOUN
ejpam-5494	20	19	by	by	ADP
ejpam-5494	20	20	assigning	assign	VERB
ejpam-5494	20	21	the	the	DET
ejpam-5494	20	22	parameter	parameter	NOUN
ejpam-5494	20	23	.	.	PUNCT
ejpam-5494	21	1	due	due	ADP
ejpam-5494	21	2	to	to	ADP
ejpam-5494	21	3	their	their	PRON
ejpam-5494	21	4	straightforward	straightforward	ADJ
ejpam-5494	21	5	use	use	NOUN
ejpam-5494	21	6	,	,	PUNCT
ejpam-5494	21	7	the	the	DET
ejpam-5494	21	8	sadik	sadik	PROPN
ejpam-5494	21	9	transformation	transformation	NOUN
ejpam-5494	21	10	has	have	AUX
ejpam-5494	21	11	continued	continue	VERB
ejpam-5494	21	12	to	to	PART
ejpam-5494	21	13	gain	gain	VERB
ejpam-5494	21	14	popularity	popularity	NOUN
ejpam-5494	21	15	among	among	ADP
ejpam-5494	21	16	academics	academic	NOUN
ejpam-5494	21	17	since	since	SCONJ
ejpam-5494	21	18	it	it	PRON
ejpam-5494	21	19	was	be	AUX
ejpam-5494	21	20	first	first	ADV
ejpam-5494	21	21	introduced	introduce	VERB
ejpam-5494	21	22	in	in	ADP
ejpam-5494	21	23	2018	2018	NUM
ejpam-5494	22	1	[	[	X
ejpam-5494	22	2	27	27	NUM
ejpam-5494	22	3	]	]	PUNCT
ejpam-5494	22	4	.	.	PUNCT
ejpam-5494	23	1	the	the	DET
ejpam-5494	23	2	advancement	advancement	NOUN
ejpam-5494	23	3	of	of	ADP
ejpam-5494	23	4	the	the	DET
ejpam-5494	23	5	transform	transform	NOUN
ejpam-5494	23	6	in	in	ADP
ejpam-5494	23	7	solving	solve	VERB
ejpam-5494	23	8	fractional	fractional	ADJ
ejpam-5494	23	9	differential	differential	ADJ
ejpam-5494	23	10	equations	equation	NOUN
ejpam-5494	23	11	is	be	AUX
ejpam-5494	23	12	found	find	VERB
ejpam-5494	23	13	in	in	ADP
ejpam-5494	23	14	much	much	ADJ
ejpam-5494	23	15	literature	literature	NOUN
ejpam-5494	23	16	and	and	CCONJ
ejpam-5494	23	17	references	reference	NOUN
ejpam-5494	23	18	therein	therein	ADV
ejpam-5494	23	19	,	,	PUNCT
ejpam-5494	23	20	such	such	ADJ
ejpam-5494	23	21	as	as	ADP
ejpam-5494	23	22	alabdala	alabdala	PROPN
ejpam-5494	23	23	et	et	PROPN
ejpam-5494	23	24	al	al	PROPN
ejpam-5494	23	25	.	.	PUNCT
ejpam-5494	24	1	[	[	X
ejpam-5494	24	2	2	2	NUM
ejpam-5494	24	3	]	]	PUNCT
ejpam-5494	24	4	used	use	VERB
ejpam-5494	24	5	the	the	DET
ejpam-5494	24	6	sadik	sadik	PROPN
ejpam-5494	24	7	transform	transform	NOUN
ejpam-5494	24	8	to	to	PART
ejpam-5494	24	9	solve	solve	VERB
ejpam-5494	24	10	the	the	DET
ejpam-5494	24	11	caputo	caputo	PROPN
ejpam-5494	24	12	delayed	delay	VERB
ejpam-5494	24	13	fractional	fractional	ADJ
ejpam-5494	24	14	differential	differential	NOUN
ejpam-5494	24	15	equation	equation	NOUN
ejpam-5494	24	16	;	;	PUNCT
ejpam-5494	24	17	derakhshan	derakhshan	PROPN
ejpam-5494	25	1	[	[	X
ejpam-5494	25	2	9	9	NUM
ejpam-5494	25	3	]	]	PUNCT
ejpam-5494	25	4	employed	employ	VERB
ejpam-5494	25	5	the	the	DET
ejpam-5494	25	6	sadik	sadik	PROPN
ejpam-5494	25	7	transform	transform	NOUN
ejpam-5494	25	8	to	to	PART
ejpam-5494	25	9	obtain	obtain	VERB
ejpam-5494	25	10	the	the	DET
ejpam-5494	25	11	solution	solution	NOUN
ejpam-5494	25	12	for	for	ADP
ejpam-5494	25	13	the	the	DET
ejpam-5494	25	14	equal	equal	ADJ
ejpam-5494	25	15	width	width	ADJ
ejpam-5494	25	16	fractional	fractional	ADJ
ejpam-5494	25	17	differential	differential	NOUN
ejpam-5494	25	18	equation	equation	NOUN
ejpam-5494	25	19	;	;	PUNCT
ejpam-5494	25	20	pue	pue	NOUN
ejpam-5494	25	21	-	-	PUNCT
ejpam-5494	25	22	on	on	ADP
ejpam-5494	25	23	[	[	X
ejpam-5494	25	24	20	20	NUM
ejpam-5494	25	25	]	]	PUNCT
ejpam-5494	25	26	utilized	utilize	VERB
ejpam-5494	25	27	the	the	DET
ejpam-5494	25	28	sadik	sadik	ADJ
ejpam-5494	25	29	decomposition	decomposition	NOUN
ejpam-5494	25	30	method	method	NOUN
ejpam-5494	25	31	to	to	PART
ejpam-5494	25	32	generate	generate	VERB
ejpam-5494	25	33	the	the	DET
ejpam-5494	25	34	solution	solution	NOUN
ejpam-5494	25	35	for	for	ADP
ejpam-5494	25	36	a	a	DET
ejpam-5494	25	37	system	system	NOUN
ejpam-5494	25	38	of	of	ADP
ejpam-5494	25	39	nonlinear	nonlinear	PROPN
ejpam-5494	25	40	fractional	fractional	PROPN
ejpam-5494	25	41	volterra	volterra	PROPN
ejpam-5494	25	42	integro	integro	PROPN
ejpam-5494	25	43	differential	differential	ADJ
ejpam-5494	25	44	equations	equation	NOUN
ejpam-5494	25	45	of	of	ADP
ejpam-5494	25	46	convolution	convolution	NOUN
ejpam-5494	25	47	type	type	NOUN
ejpam-5494	25	48	;	;	PUNCT
ejpam-5494	25	49	pue	pue	NOUN
ejpam-5494	25	50	-	-	PUNCT
ejpam-5494	25	51	on	on	ADP
ejpam-5494	25	52	[	[	X
ejpam-5494	25	53	21	21	NUM
ejpam-5494	25	54	]	]	PUNCT
ejpam-5494	25	55	,	,	PUNCT
ejpam-5494	26	1	[	[	X
ejpam-5494	26	2	22	22	NUM
ejpam-5494	26	3	]	]	PUNCT
ejpam-5494	26	4	also	also	ADV
ejpam-5494	26	5	obtained	obtain	VERB
ejpam-5494	26	6	the	the	DET
ejpam-5494	26	7	solution	solution	NOUN
ejpam-5494	26	8	of	of	ADP
ejpam-5494	26	9	the	the	DET
ejpam-5494	26	10	space	space	NOUN
ejpam-5494	26	11	and	and	CCONJ
ejpam-5494	26	12	time	time	NOUN
ejpam-5494	26	13	fractional	fractional	PROPN
ejpam-5494	26	14	telegraph	telegraph	NOUN
ejpam-5494	26	15	equation	equation	NOUN
ejpam-5494	26	16	and	and	CCONJ
ejpam-5494	26	17	well	well	ADV
ejpam-5494	26	18	-	-	PUNCT
ejpam-5494	26	19	known	know	VERB
ejpam-5494	26	20	fractional	fractional	ADJ
ejpam-5494	26	21	partial	partial	ADJ
ejpam-5494	26	22	differential	differential	NOUN
ejpam-5494	26	23	equation	equation	NOUN
ejpam-5494	26	24	by	by	ADP
ejpam-5494	26	25	double	double	ADJ
ejpam-5494	26	26	sadik	sadik	PROPN
ejpam-5494	26	27	transform	transform	NOUN
ejpam-5494	26	28	.	.	PUNCT
ejpam-5494	27	1	the	the	DET
ejpam-5494	27	2	residual	residual	ADJ
ejpam-5494	27	3	power	power	NOUN
ejpam-5494	27	4	series	series	PROPN
ejpam-5494	27	5	approach	approach	NOUN
ejpam-5494	27	6	is	be	AUX
ejpam-5494	27	7	a	a	DET
ejpam-5494	27	8	highly	highly	ADV
ejpam-5494	27	9	effective	effective	ADJ
ejpam-5494	27	10	semi	semi	ADJ
ejpam-5494	27	11	-	-	ADJ
ejpam-5494	27	12	analytic	analytic	ADJ
ejpam-5494	27	13	procedure	procedure	NOUN
ejpam-5494	27	14	for	for	ADP
ejpam-5494	27	15	handling	handle	VERB
ejpam-5494	27	16	scientific	scientific	ADJ
ejpam-5494	27	17	challenges	challenge	NOUN
ejpam-5494	27	18	.	.	PUNCT
ejpam-5494	28	1	the	the	DET
ejpam-5494	28	2	aforementioned	aforementioned	ADJ
ejpam-5494	28	3	strategy	strategy	NOUN
ejpam-5494	28	4	is	be	AUX
ejpam-5494	28	5	based	base	VERB
ejpam-5494	28	6	on	on	ADP
ejpam-5494	28	7	the	the	DET
ejpam-5494	28	8	generalized	generalize	VERB
ejpam-5494	28	9	taylor	taylor	PROPN
ejpam-5494	28	10	series	series	PROPN
ejpam-5494	28	11	expansion	expansion	NOUN
ejpam-5494	28	12	.	.	PUNCT
ejpam-5494	29	1	the	the	DET
ejpam-5494	29	2	concept	concept	NOUN
ejpam-5494	29	3	is	be	AUX
ejpam-5494	29	4	to	to	PART
ejpam-5494	29	5	view	view	VERB
ejpam-5494	29	6	the	the	DET
ejpam-5494	29	7	solution	solution	NOUN
ejpam-5494	29	8	as	as	ADP
ejpam-5494	29	9	a	a	DET
ejpam-5494	29	10	fractional	fractional	ADJ
ejpam-5494	29	11	power	power	NOUN
ejpam-5494	29	12	series	series	NOUN
ejpam-5494	29	13	with	with	ADP
ejpam-5494	29	14	unknown	unknown	ADJ
ejpam-5494	29	15	coefficients	coefficient	NOUN
ejpam-5494	29	16	and	and	CCONJ
ejpam-5494	29	17	establish	establish	VERB
ejpam-5494	29	18	a	a	DET
ejpam-5494	29	19	residual	residual	ADJ
ejpam-5494	29	20	function	function	NOUN
ejpam-5494	29	21	.	.	PUNCT
ejpam-5494	30	1	a	a	DET
ejpam-5494	30	2	traditional	traditional	ADJ
ejpam-5494	30	3	residual	residual	ADJ
ejpam-5494	30	4	power	power	NOUN
ejpam-5494	30	5	series	series	NOUN
ejpam-5494	30	6	method	method	NOUN
ejpam-5494	30	7	and	and	CCONJ
ejpam-5494	30	8	an	an	DET
ejpam-5494	30	9	improved	improved	ADJ
ejpam-5494	30	10	version	version	NOUN
ejpam-5494	30	11	have	have	AUX
ejpam-5494	30	12	been	be	AUX
ejpam-5494	30	13	widely	widely	ADV
ejpam-5494	30	14	utilized	utilize	VERB
ejpam-5494	30	15	in	in	ADP
ejpam-5494	30	16	literature	literature	NOUN
ejpam-5494	30	17	to	to	PART
ejpam-5494	30	18	address	address	VERB
ejpam-5494	30	19	a	a	DET
ejpam-5494	30	20	system	system	NOUN
ejpam-5494	30	21	of	of	ADP
ejpam-5494	30	22	fractional	fractional	ADJ
ejpam-5494	30	23	differential	differential	ADJ
ejpam-5494	30	24	equations	equation	NOUN
ejpam-5494	30	25	,	,	PUNCT
ejpam-5494	30	26	both	both	CCONJ
ejpam-5494	30	27	linear	linear	ADJ
ejpam-5494	30	28	and	and	CCONJ
ejpam-5494	30	29	non	non	ADJ
ejpam-5494	30	30	-	-	ADJ
ejpam-5494	30	31	linear	linear	ADJ
ejpam-5494	30	32	.	.	PUNCT
ejpam-5494	31	1	recently	recently	ADV
ejpam-5494	31	2	,	,	PUNCT
ejpam-5494	31	3	some	some	PRON
ejpam-5494	31	4	of	of	ADP
ejpam-5494	31	5	these	these	DET
ejpam-5494	31	6	developments	development	NOUN
ejpam-5494	31	7	in	in	ADP
ejpam-5494	31	8	non	non	ADJ
ejpam-5494	31	9	-	-	ADJ
ejpam-5494	31	10	linear	linear	ADJ
ejpam-5494	31	11	system	system	NOUN
ejpam-5494	31	12	can	can	AUX
ejpam-5494	31	13	be	be	AUX
ejpam-5494	31	14	observed	observe	VERB
ejpam-5494	31	15	in	in	ADP
ejpam-5494	31	16	[	[	X
ejpam-5494	31	17	3	3	NUM
ejpam-5494	31	18	]	]	PUNCT
ejpam-5494	31	19	,	,	PUNCT
ejpam-5494	31	20	[	[	X
ejpam-5494	31	21	5	5	NUM
ejpam-5494	31	22	]	]	PUNCT
ejpam-5494	31	23	,	,	PUNCT
ejpam-5494	31	24	[	[	X
ejpam-5494	31	25	13	13	NUM
ejpam-5494	31	26	]	]	PUNCT
ejpam-5494	31	27	,	,	PUNCT
ejpam-5494	31	28	[	[	X
ejpam-5494	31	29	14	14	NUM
ejpam-5494	31	30	]	]	PUNCT
ejpam-5494	31	31	and	and	CCONJ
ejpam-5494	31	32	[	[	X
ejpam-5494	31	33	23	23	NUM
ejpam-5494	31	34	]	]	PUNCT
ejpam-5494	31	35	.	.	PUNCT
ejpam-5494	32	1	the	the	DET
ejpam-5494	32	2	inspiration	inspiration	NOUN
ejpam-5494	32	3	for	for	ADP
ejpam-5494	32	4	this	this	DET
ejpam-5494	32	5	work	work	NOUN
ejpam-5494	32	6	was	be	AUX
ejpam-5494	32	7	to	to	PART
ejpam-5494	32	8	devise	devise	VERB
ejpam-5494	32	9	an	an	DET
ejpam-5494	32	10	analytical	analytical	ADJ
ejpam-5494	32	11	method	method	NOUN
ejpam-5494	32	12	that	that	PRON
ejpam-5494	32	13	leveraged	leverage	VERB
ejpam-5494	32	14	two	two	NUM
ejpam-5494	32	15	widely	widely	ADV
ejpam-5494	32	16	recognized	recognize	VERB
ejpam-5494	32	17	mathematical	mathematical	ADJ
ejpam-5494	32	18	tools	tool	NOUN
ejpam-5494	32	19	,	,	PUNCT
ejpam-5494	32	20	the	the	DET
ejpam-5494	32	21	sadik	sadik	ADJ
ejpam-5494	32	22	integral	integral	ADJ
ejpam-5494	32	23	transform	transform	NOUN
ejpam-5494	32	24	and	and	CCONJ
ejpam-5494	32	25	the	the	DET
ejpam-5494	32	26	residual	residual	ADJ
ejpam-5494	32	27	power	power	NOUN
ejpam-5494	32	28	series	series	NOUN
ejpam-5494	32	29	technique	technique	NOUN
ejpam-5494	32	30	,	,	PUNCT
ejpam-5494	32	31	to	to	PART
ejpam-5494	32	32	solve	solve	VERB
ejpam-5494	32	33	a	a	DET
ejpam-5494	32	34	nonlinear	nonlinear	ADJ
ejpam-5494	32	35	system	system	NOUN
ejpam-5494	32	36	of	of	ADP
ejpam-5494	32	37	fractional	fractional	ADJ
ejpam-5494	32	38	order	order	NOUN
ejpam-5494	32	39	differential	differential	NOUN
ejpam-5494	32	40	equations	equation	NOUN
ejpam-5494	32	41	.	.	PUNCT
ejpam-5494	33	1	the	the	DET
ejpam-5494	33	2	primary	primary	ADJ
ejpam-5494	33	3	objective	objective	NOUN
ejpam-5494	33	4	of	of	ADP
ejpam-5494	33	5	the	the	DET
ejpam-5494	33	6	current	current	ADJ
ejpam-5494	33	7	study	study	NOUN
ejpam-5494	33	8	is	be	AUX
ejpam-5494	33	9	to	to	PART
ejpam-5494	33	10	deploy	deploy	VERB
ejpam-5494	33	11	the	the	DET
ejpam-5494	33	12	sadik	sadik	PROPN
ejpam-5494	33	13	residual	residual	ADJ
ejpam-5494	33	14	power	power	NOUN
ejpam-5494	33	15	series	series	PROPN
ejpam-5494	33	16	approach	approach	NOUN
ejpam-5494	33	17	to	to	PART
ejpam-5494	33	18	solve	solve	VERB
ejpam-5494	33	19	the	the	DET
ejpam-5494	33	20	initial	initial	ADJ
ejpam-5494	33	21	value	value	NOUN
ejpam-5494	33	22	problem	problem	NOUN
ejpam-5494	33	23	for	for	ADP
ejpam-5494	33	24	a	a	DET
ejpam-5494	33	25	system	system	NOUN
ejpam-5494	33	26	of	of	ADP
ejpam-5494	33	27	nonlinear	nonlinear	PROPN
ejpam-5494	33	28	caputo	caputo	PROPN
ejpam-5494	33	29	fractional	fractional	PROPN
ejpam-5494	33	30	partial	partial	ADJ
ejpam-5494	33	31	differential	differential	NOUN
ejpam-5494	33	32	equations	equation	NOUN
ejpam-5494	33	33	with	with	ADP
ejpam-5494	33	34	the	the	DET
ejpam-5494	33	35	form	form	NOUN
ejpam-5494	33	36	dγ	dγ	ADP
ejpam-5494	33	37	t	t	PROPN
ejpam-5494	33	38	ui(x	ui(x	PROPN
ejpam-5494	33	39	,	,	PUNCT
ejpam-5494	33	40	t	t	PROPN
ejpam-5494	33	41	)	)	PUNCT
ejpam-5494	33	42	=	=	SYM
ejpam-5494	33	43	ni(uj(x	ni(uj(x	PROPN
ejpam-5494	33	44	,	,	PUNCT
ejpam-5494	33	45	t),x	t),x	PROPN
ejpam-5494	33	46	,	,	PUNCT
ejpam-5494	33	47	t	t	PROPN
ejpam-5494	33	48	)	)	PUNCT
ejpam-5494	33	49	+	+	SYM
ejpam-5494	33	50	fi(x	fi(x	NUM
ejpam-5494	33	51	,	,	PUNCT
ejpam-5494	33	52	t	t	PROPN
ejpam-5494	33	53	)	)	PUNCT
ejpam-5494	33	54	,	,	PUNCT
ejpam-5494	33	55	i	i	PRON
ejpam-5494	33	56	=	=	NOUN
ejpam-5494	33	57	1	1	NUM
ejpam-5494	33	58	,	,	PUNCT
ejpam-5494	33	59	.	.	PUNCT
ejpam-5494	33	60	.	.	PUNCT
ejpam-5494	34	1	.	.	PUNCT
ejpam-5494	35	1	,	,	PUNCT
ejpam-5494	35	2	n	n	CCONJ
ejpam-5494	35	3	(	(	PUNCT
ejpam-5494	35	4	1	1	NUM
ejpam-5494	35	5	)	)	PUNCT
ejpam-5494	35	6	ui(x	ui(x	ADJ
ejpam-5494	35	7	,	,	PUNCT
ejpam-5494	35	8	0	0	NUM
ejpam-5494	35	9	)	)	PUNCT
ejpam-5494	35	10	=	=	SYM
ejpam-5494	35	11	gi(x	gi(x	PROPN
ejpam-5494	35	12	)	)	PUNCT
ejpam-5494	35	13	.	.	PUNCT
ejpam-5494	36	1	(	(	PUNCT
ejpam-5494	36	2	2	2	NUM
ejpam-5494	36	3	)	)	PUNCT
ejpam-5494	36	4	0	0	PUNCT
ejpam-5494	37	1	<	<	X
ejpam-5494	37	2	γ	γ	X
ejpam-5494	37	3	⩽	⩽	PROPN
ejpam-5494	37	4	1	1	X
ejpam-5494	37	5	.	.	PUNCT
ejpam-5494	37	6	here	here	ADV
ejpam-5494	37	7	dγ	dγ	ADP
ejpam-5494	37	8	t	t	PROPN
ejpam-5494	37	9	(	(	PUNCT
ejpam-5494	37	10	·	·	PUNCT
ejpam-5494	37	11	)	)	PUNCT
ejpam-5494	37	12	denotes	denote	VERB
ejpam-5494	37	13	the	the	DET
ejpam-5494	37	14	caputo	caputo	PROPN
ejpam-5494	37	15	partial	partial	ADJ
ejpam-5494	37	16	fractional	fractional	ADJ
ejpam-5494	37	17	derivative	derivative	NOUN
ejpam-5494	37	18	of	of	ADP
ejpam-5494	37	19	order	order	NOUN
ejpam-5494	37	20	γ	γ	X
ejpam-5494	37	21	,	,	PUNCT
ejpam-5494	37	22	ni	ni	PROPN
ejpam-5494	37	23	represents	represent	VERB
ejpam-5494	37	24	the	the	DET
ejpam-5494	37	25	general	general	ADJ
ejpam-5494	37	26	nonlinear	nonlinear	ADJ
ejpam-5494	37	27	differential	differential	NOUN
ejpam-5494	37	28	operator	operator	NOUN
ejpam-5494	37	29	and	and	CCONJ
ejpam-5494	37	30	fi	fi	NOUN
ejpam-5494	37	31	is	be	AUX
ejpam-5494	37	32	the	the	DET
ejpam-5494	37	33	source	source	NOUN
ejpam-5494	37	34	term	term	NOUN
ejpam-5494	37	35	.	.	PUNCT
ejpam-5494	38	1	this	this	DET
ejpam-5494	38	2	system	system	NOUN
ejpam-5494	38	3	is	be	AUX
ejpam-5494	38	4	highly	highly	ADV
ejpam-5494	38	5	significant	significant	ADJ
ejpam-5494	38	6	in	in	ADP
ejpam-5494	38	7	the	the	DET
ejpam-5494	38	8	fields	field	NOUN
ejpam-5494	38	9	of	of	ADP
ejpam-5494	38	10	science	science	NOUN
ejpam-5494	38	11	and	and	CCONJ
ejpam-5494	38	12	technology	technology	NOUN
ejpam-5494	38	13	.	.	PUNCT
ejpam-5494	39	1	the	the	DET
ejpam-5494	39	2	structure	structure	NOUN
ejpam-5494	39	3	of	of	ADP
ejpam-5494	39	4	the	the	DET
ejpam-5494	39	5	manuscript	manuscript	NOUN
ejpam-5494	39	6	is	be	AUX
ejpam-5494	39	7	designed	design	VERB
ejpam-5494	39	8	as	as	SCONJ
ejpam-5494	39	9	follows	follow	VERB
ejpam-5494	39	10	:	:	PUNCT
ejpam-5494	39	11	section	section	NOUN
ejpam-5494	39	12	2	2	NUM
ejpam-5494	39	13	presents	present	VERB
ejpam-5494	39	14	fundamental	fundamental	ADJ
ejpam-5494	39	15	definitions	definition	NOUN
ejpam-5494	39	16	and	and	CCONJ
ejpam-5494	39	17	theorems	theorem	NOUN
ejpam-5494	39	18	of	of	ADP
ejpam-5494	39	19	fractional	fractional	ADJ
ejpam-5494	39	20	calculus	calculus	NOUN
ejpam-5494	39	21	,	,	PUNCT
ejpam-5494	39	22	the	the	DET
ejpam-5494	39	23	sadik	sadik	PROPN
ejpam-5494	39	24	transform	transform	NOUN
ejpam-5494	39	25	,	,	PUNCT
ejpam-5494	39	26	and	and	CCONJ
ejpam-5494	39	27	the	the	DET
ejpam-5494	39	28	residual	residual	ADJ
ejpam-5494	39	29	power	power	NOUN
ejpam-5494	39	30	series	series	NOUN
ejpam-5494	39	31	method	method	NOUN
ejpam-5494	39	32	.	.	PUNCT
ejpam-5494	40	1	these	these	DET
ejpam-5494	40	2	theoretical	theoretical	ADJ
ejpam-5494	40	3	foundations	foundation	NOUN
ejpam-5494	40	4	support	support	VERB
ejpam-5494	40	5	the	the	DET
ejpam-5494	40	6	methodology	methodology	NOUN
ejpam-5494	40	7	employed	employ	VERB
ejpam-5494	40	8	in	in	ADP
ejpam-5494	40	9	this	this	DET
ejpam-5494	40	10	study	study	NOUN
ejpam-5494	40	11	.	.	PUNCT
ejpam-5494	41	1	section	section	NOUN
ejpam-5494	41	2	3	3	NUM
ejpam-5494	41	3	describes	describe	VERB
ejpam-5494	41	4	the	the	DET
ejpam-5494	41	5	implementation	implementation	NOUN
ejpam-5494	41	6	of	of	ADP
ejpam-5494	41	7	the	the	DET
ejpam-5494	41	8	sadik	sadik	PROPN
ejpam-5494	41	9	residual	residual	ADJ
ejpam-5494	41	10	power	power	NOUN
ejpam-5494	41	11	series	series	PROPN
ejpam-5494	41	12	method	method	NOUN
ejpam-5494	41	13	to	to	ADP
ejpam-5494	41	14	nonlinear	nonlinear	ADJ
ejpam-5494	41	15	systems	system	NOUN
ejpam-5494	41	16	of	of	ADP
ejpam-5494	41	17	fractional	fractional	ADJ
ejpam-5494	41	18	partial	partial	ADJ
ejpam-5494	41	19	differential	differential	NOUN
ejpam-5494	41	20	equations	equation	NOUN
ejpam-5494	41	21	.	.	PUNCT
ejpam-5494	42	1	this	this	DET
ejpam-5494	42	2	section	section	NOUN
ejpam-5494	42	3	p.	p.	NOUN
ejpam-5494	42	4	pue	pue	PROPN
ejpam-5494	42	5	-	-	PUNCT
ejpam-5494	42	6	on	on	ADP
ejpam-5494	42	7	/	/	SYM
ejpam-5494	42	8	eur	eur	NOUN
ejpam-5494	42	9	.	.	PUNCT
ejpam-5494	43	1	j.	j.	PROPN
ejpam-5494	43	2	pure	pure	PROPN
ejpam-5494	43	3	appl	appl	PROPN
ejpam-5494	43	4	.	.	PROPN
ejpam-5494	43	5	math	math	PROPN
ejpam-5494	43	6	,	,	PUNCT
ejpam-5494	43	7	17	17	NUM
ejpam-5494	43	8	(	(	PUNCT
ejpam-5494	43	9	4	4	NUM
ejpam-5494	43	10	)	)	PUNCT
ejpam-5494	43	11	(	(	PUNCT
ejpam-5494	43	12	2024	2024	NUM
ejpam-5494	43	13	)	)	PUNCT
ejpam-5494	43	14	,	,	PUNCT
ejpam-5494	43	15	3826	3826	NUM
ejpam-5494	43	16	-	-	SYM
ejpam-5494	43	17	3846	3846	NUM
ejpam-5494	43	18	3828	3828	NUM
ejpam-5494	43	19	also	also	ADV
ejpam-5494	43	20	comprises	comprise	VERB
ejpam-5494	43	21	illustrative	illustrative	ADJ
ejpam-5494	43	22	examples	example	NOUN
ejpam-5494	43	23	that	that	PRON
ejpam-5494	43	24	serve	serve	VERB
ejpam-5494	43	25	to	to	PART
ejpam-5494	43	26	demonstrate	demonstrate	VERB
ejpam-5494	43	27	and	and	CCONJ
ejpam-5494	43	28	validate	validate	VERB
ejpam-5494	43	29	the	the	DET
ejpam-5494	43	30	proposed	propose	VERB
ejpam-5494	43	31	technique	technique	NOUN
ejpam-5494	43	32	.	.	PUNCT
ejpam-5494	44	1	section	section	NOUN
ejpam-5494	44	2	4	4	NUM
ejpam-5494	44	3	shows	show	VERB
ejpam-5494	44	4	a	a	DET
ejpam-5494	44	5	comprehensive	comprehensive	ADJ
ejpam-5494	44	6	discussion	discussion	NOUN
ejpam-5494	44	7	of	of	ADP
ejpam-5494	44	8	the	the	DET
ejpam-5494	44	9	findings	finding	NOUN
ejpam-5494	44	10	and	and	CCONJ
ejpam-5494	44	11	presents	present	VERB
ejpam-5494	44	12	the	the	DET
ejpam-5494	44	13	conclusions	conclusion	NOUN
ejpam-5494	44	14	from	from	ADP
ejpam-5494	44	15	this	this	DET
ejpam-5494	44	16	research	research	NOUN
ejpam-5494	44	17	.	.	PUNCT
ejpam-5494	45	1	2	2	X
ejpam-5494	45	2	.	.	X
ejpam-5494	45	3	basic	basic	ADJ
ejpam-5494	45	4	definitions	definition	NOUN
ejpam-5494	45	5	and	and	CCONJ
ejpam-5494	45	6	theorems	theorem	NOUN
ejpam-5494	45	7	of	of	ADP
ejpam-5494	45	8	fractional	fractional	ADJ
ejpam-5494	45	9	calculus	calculus	NOUN
ejpam-5494	45	10	,	,	PUNCT
ejpam-5494	45	11	sadik	sadik	ADJ
ejpam-5494	45	12	integral	integral	ADJ
ejpam-5494	45	13	transform	transform	NOUN
ejpam-5494	45	14	and	and	CCONJ
ejpam-5494	45	15	residual	residual	ADJ
ejpam-5494	45	16	power	power	NOUN
ejpam-5494	45	17	series	series	NOUN
ejpam-5494	45	18	method	method	VERB
ejpam-5494	45	19	this	this	DET
ejpam-5494	45	20	section	section	NOUN
ejpam-5494	45	21	reviews	review	VERB
ejpam-5494	45	22	the	the	DET
ejpam-5494	45	23	basic	basic	ADJ
ejpam-5494	45	24	notions	notion	NOUN
ejpam-5494	45	25	and	and	CCONJ
ejpam-5494	45	26	essential	essential	ADJ
ejpam-5494	45	27	properties	property	NOUN
ejpam-5494	45	28	of	of	ADP
ejpam-5494	45	29	fractional	fractional	ADJ
ejpam-5494	45	30	calculus	calculus	NOUN
ejpam-5494	45	31	.	.	PUNCT
ejpam-5494	46	1	furthermore	furthermore	ADV
ejpam-5494	46	2	,	,	PUNCT
ejpam-5494	46	3	the	the	DET
ejpam-5494	46	4	definitions	definition	NOUN
ejpam-5494	46	5	and	and	CCONJ
ejpam-5494	46	6	theorems	theorem	NOUN
ejpam-5494	46	7	of	of	ADP
ejpam-5494	46	8	the	the	DET
ejpam-5494	46	9	sadik	sadik	ADJ
ejpam-5494	46	10	integral	integral	ADJ
ejpam-5494	46	11	transform	transform	NOUN
ejpam-5494	46	12	and	and	CCONJ
ejpam-5494	46	13	residual	residual	ADJ
ejpam-5494	46	14	power	power	NOUN
ejpam-5494	46	15	series	series	NOUN
ejpam-5494	46	16	technique	technique	NOUN
ejpam-5494	46	17	are	be	AUX
ejpam-5494	46	18	discussed	discuss	VERB
ejpam-5494	46	19	.	.	PUNCT
ejpam-5494	47	1	2.1	2.1	NUM
ejpam-5494	47	2	.	.	PUNCT
ejpam-5494	47	3	fractional	fractional	ADJ
ejpam-5494	47	4	calculus	calculus	NOUN
ejpam-5494	47	5	definition	definition	NOUN
ejpam-5494	47	6	1	1	NUM
ejpam-5494	47	7	.	.	PUNCT
ejpam-5494	48	1	[	[	X
ejpam-5494	48	2	18	18	NUM
ejpam-5494	48	3	]	]	PUNCT
ejpam-5494	48	4	the	the	DET
ejpam-5494	48	5	fractional	fractional	ADJ
ejpam-5494	48	6	integral	integral	ADJ
ejpam-5494	48	7	operator	operator	NOUN
ejpam-5494	48	8	of	of	ADP
ejpam-5494	48	9	order	order	NOUN
ejpam-5494	48	10	γ(γ	γ(γ	PUNCT
ejpam-5494	48	11	⩾	⩾	PROPN
ejpam-5494	48	12	0	0	NUM
ejpam-5494	48	13	)	)	PUNCT
ejpam-5494	48	14	of	of	ADP
ejpam-5494	48	15	ϕ(t	ϕ(t	NUM
ejpam-5494	48	16	)	)	PUNCT
ejpam-5494	48	17	of	of	ADP
ejpam-5494	48	18	riemannliouville	riemannliouville	NOUN
ejpam-5494	48	19	type	type	NOUN
ejpam-5494	48	20	is	be	AUX
ejpam-5494	48	21	defined	define	VERB
ejpam-5494	48	22	as	as	ADP
ejpam-5494	48	23	iγϕ(t	iγϕ(t	PROPN
ejpam-5494	48	24	)	)	PUNCT
ejpam-5494	48	25	=	=	PUNCT
ejpam-5494	49	1			PUNCT
ejpam-5494	49	2	1	1	NUM
ejpam-5494	49	3	γ(γ	γ(γ	NOUN
ejpam-5494	49	4	)	)	PUNCT
ejpam-5494	50	1	∫	∫	PROPN
ejpam-5494	50	2	t	t	PROPN
ejpam-5494	50	3	0	0	NUM
ejpam-5494	50	4	ϕ(τ	ϕ(τ	PROPN
ejpam-5494	50	5	)	)	PUNCT
ejpam-5494	50	6	(	(	PUNCT
ejpam-5494	50	7	t−	t−	PROPN
ejpam-5494	50	8	τ)1−γ	τ)1−γ	PROPN
ejpam-5494	50	9	dτ	dτ	PROPN
ejpam-5494	50	10	,	,	PUNCT
ejpam-5494	50	11	γ	γ	X
ejpam-5494	50	12	>	>	X
ejpam-5494	50	13	0	0	PROPN
ejpam-5494	50	14	,	,	PUNCT
ejpam-5494	50	15	t	t	X
ejpam-5494	50	16	>	>	X
ejpam-5494	50	17	0	0	PROPN
ejpam-5494	50	18	,	,	PUNCT
ejpam-5494	50	19	ϕ(t	ϕ(t	NUM
ejpam-5494	50	20	)	)	PUNCT
ejpam-5494	50	21	,	,	PUNCT
ejpam-5494	50	22	γ	γ	X
ejpam-5494	50	23	=	=	SYM
ejpam-5494	50	24	0	0	NUM
ejpam-5494	50	25	definition	definition	NOUN
ejpam-5494	50	26	2	2	NUM
ejpam-5494	50	27	.	.	PUNCT
ejpam-5494	51	1	the	the	DET
ejpam-5494	51	2	caputo	caputo	PROPN
ejpam-5494	51	3	fractional	fractional	PROPN
ejpam-5494	51	4	derivative	derivative	ADJ
ejpam-5494	51	5	operator	operator	NOUN
ejpam-5494	51	6	dγ	dγ	NOUN
ejpam-5494	51	7	of	of	ADP
ejpam-5494	51	8	order	order	NOUN
ejpam-5494	51	9	γ	γ	X
ejpam-5494	51	10	,	,	PUNCT
ejpam-5494	51	11	(	(	PUNCT
ejpam-5494	51	12	n	n	CCONJ
ejpam-5494	51	13	−	−	PROPN
ejpam-5494	51	14	1	1	NUM
ejpam-5494	51	15	<	<	X
ejpam-5494	51	16	γ	γ	X
ejpam-5494	51	17	⩽	⩽	PROPN
ejpam-5494	51	18	n	n	CCONJ
ejpam-5494	51	19	,	,	PUNCT
ejpam-5494	51	20	n	n	CCONJ
ejpam-5494	51	21	∈	∈	PROPN
ejpam-5494	51	22	n	n	CCONJ
ejpam-5494	51	23	)	)	PUNCT
ejpam-5494	51	24	is	be	AUX
ejpam-5494	51	25	defined	define	VERB
ejpam-5494	51	26	in	in	ADP
ejpam-5494	51	27	the	the	DET
ejpam-5494	51	28	following	follow	VERB
ejpam-5494	51	29	form	form	NOUN
ejpam-5494	51	30	,	,	PUNCT
ejpam-5494	51	31	dγϕ(t	dγϕ(t	PROPN
ejpam-5494	51	32	)	)	PUNCT
ejpam-5494	51	33	=	=	SYM
ejpam-5494	52	1	1	1	NUM
ejpam-5494	52	2	γ(n−	γ(n−	PROPN
ejpam-5494	52	3	γ	γ	PROPN
ejpam-5494	52	4	)	)	PUNCT
ejpam-5494	52	5	∫	∫	PROPN
ejpam-5494	52	6	t	t	PROPN
ejpam-5494	52	7	0	0	NUM
ejpam-5494	53	1	(	(	PUNCT
ejpam-5494	53	2	t−	t−	PROPN
ejpam-5494	53	3	τ)−γ+n−1ϕ(n)(τ)dτ	τ)−γ+n−1ϕ(n)(τ)dτ	PROPN
ejpam-5494	53	4	,	,	PUNCT
ejpam-5494	53	5	(	(	PUNCT
ejpam-5494	53	6	3	3	X
ejpam-5494	53	7	)	)	PUNCT
ejpam-5494	53	8	γ	γ	X
ejpam-5494	53	9	>	>	X
ejpam-5494	53	10	0	0	PROPN
ejpam-5494	53	11	,	,	PUNCT
ejpam-5494	53	12	t	t	X
ejpam-5494	53	13	>	>	X
ejpam-5494	53	14	0	0	PROPN
ejpam-5494	53	15	,	,	PUNCT
ejpam-5494	53	16	where	where	SCONJ
ejpam-5494	53	17	the	the	DET
ejpam-5494	53	18	function	function	NOUN
ejpam-5494	53	19	ϕ(t	ϕ(t	NUM
ejpam-5494	53	20	)	)	PUNCT
ejpam-5494	53	21	has	have	VERB
ejpam-5494	53	22	absolutely	absolutely	ADV
ejpam-5494	53	23	continuous	continuous	ADJ
ejpam-5494	53	24	derivatives	derivative	NOUN
ejpam-5494	53	25	up	up	ADP
ejpam-5494	53	26	to	to	PART
ejpam-5494	53	27	order	order	VERB
ejpam-5494	53	28	n−	n−	NOUN
ejpam-5494	53	29	1	1	NUM
ejpam-5494	53	30	.	.	PUNCT
ejpam-5494	54	1	moreover	moreover	ADV
ejpam-5494	54	2	,	,	PUNCT
ejpam-5494	54	3	the	the	DET
ejpam-5494	54	4	following	follow	VERB
ejpam-5494	54	5	basic	basic	ADJ
ejpam-5494	54	6	properties	property	NOUN
ejpam-5494	54	7	can	can	AUX
ejpam-5494	54	8	be	be	AUX
ejpam-5494	54	9	proved	prove	VERB
ejpam-5494	54	10	1	1	NUM
ejpam-5494	54	11	.	.	PUNCT
ejpam-5494	54	12	)	)	PUNCT
ejpam-5494	54	13	dγc	dγc	NOUN
ejpam-5494	55	1	=	=	SYM
ejpam-5494	55	2	0	0	NUM
ejpam-5494	55	3	,	,	PUNCT
ejpam-5494	55	4	c	c	PROPN
ejpam-5494	55	5	is	be	AUX
ejpam-5494	55	6	a	a	DET
ejpam-5494	55	7	constant	constant	ADJ
ejpam-5494	55	8	2	2	NUM
ejpam-5494	55	9	.	.	PUNCT
ejpam-5494	55	10	)	)	PUNCT
ejpam-5494	56	1	for	for	ADP
ejpam-5494	56	2	p	p	PROPN
ejpam-5494	56	3	∈	∈	PROPN
ejpam-5494	56	4	n0	n0	X
ejpam-5494	56	5	=	=	SYM
ejpam-5494	56	6	{	{	PUNCT
ejpam-5494	56	7	0	0	NUM
ejpam-5494	56	8	,	,	PUNCT
ejpam-5494	56	9	1	1	NUM
ejpam-5494	56	10	,	,	PUNCT
ejpam-5494	56	11	2	2	NUM
ejpam-5494	56	12	,	,	PUNCT
ejpam-5494	56	13	.	.	PUNCT
ejpam-5494	56	14	.	.	PUNCT
ejpam-5494	56	15	.	.	PUNCT
ejpam-5494	56	16	}	}	PUNCT
ejpam-5494	57	1	and	and	CCONJ
ejpam-5494	57	2	the	the	DET
ejpam-5494	57	3	ceiling	ceiling	NOUN
ejpam-5494	57	4	function	function	NOUN
ejpam-5494	57	5	⌈γ⌉	⌈γ⌉	NOUN
ejpam-5494	57	6	refers	refer	VERB
ejpam-5494	57	7	to	to	ADP
ejpam-5494	57	8	the	the	DET
ejpam-5494	57	9	smallest	small	ADJ
ejpam-5494	57	10	integer	integer	NOUN
ejpam-5494	57	11	greater	great	ADJ
ejpam-5494	57	12	than	than	ADP
ejpam-5494	57	13	or	or	CCONJ
ejpam-5494	57	14	equal	equal	ADJ
ejpam-5494	57	15	to	to	ADP
ejpam-5494	57	16	γ	γ	PROPN
ejpam-5494	57	17	dγxp	dγxp	NOUN
ejpam-5494	57	18	=	=	PUNCT
ejpam-5494	57	19			PROPN
ejpam-5494	57	20	0	0	NUM
ejpam-5494	57	21	,	,	PUNCT
ejpam-5494	57	22	for	for	ADP
ejpam-5494	57	23	p	p	NOUN
ejpam-5494	57	24	<	<	X
ejpam-5494	57	25	⌈γ⌉	⌈γ⌉	X
ejpam-5494	57	26	γ(p+	γ(p+	PROPN
ejpam-5494	57	27	1	1	NUM
ejpam-5494	57	28	)	)	PUNCT
ejpam-5494	57	29	γ(p+	γ(p+	PROPN
ejpam-5494	57	30	1−	1−	NUM
ejpam-5494	57	31	γ	γ	X
ejpam-5494	57	32	)	)	PUNCT
ejpam-5494	57	33	xp−γ	xp−γ	PROPN
ejpam-5494	57	34	,	,	PUNCT
ejpam-5494	57	35	for	for	ADP
ejpam-5494	57	36	p	p	PROPN
ejpam-5494	58	1	⩾	⩾	PROPN
ejpam-5494	58	2	⌈γ⌉	⌈γ⌉	NOUN
ejpam-5494	58	3	3	3	NUM
ejpam-5494	58	4	.	.	PUNCT
ejpam-5494	58	5	)	)	PUNCT
ejpam-5494	59	1	dγiγϕ(t	dγiγϕ(t	PROPN
ejpam-5494	59	2	)	)	PUNCT
ejpam-5494	59	3	=	=	SYM
ejpam-5494	59	4	ϕ(t	ϕ(t	PROPN
ejpam-5494	59	5	)	)	PUNCT
ejpam-5494	59	6	,	,	PUNCT
ejpam-5494	59	7	4	4	NUM
ejpam-5494	59	8	.	.	PUNCT
ejpam-5494	59	9	)	)	PUNCT
ejpam-5494	59	10	iγdγϕ(t	iγdγϕ(t	NOUN
ejpam-5494	59	11	)	)	PUNCT
ejpam-5494	59	12	=	=	SYM
ejpam-5494	60	1	ϕ(t)−	ϕ(t)−	PROPN
ejpam-5494	60	2	n−1∑	n−1∑	NUM
ejpam-5494	60	3	k=1	k=1	PROPN
ejpam-5494	60	4	ϕ(k)(0	ϕ(k)(0	NUM
ejpam-5494	60	5	)	)	PUNCT
ejpam-5494	61	1	k	k	PROPN
ejpam-5494	61	2	!	!	PUNCT
ejpam-5494	61	3	tk	tk	PROPN
ejpam-5494	61	4	.	.	PUNCT
ejpam-5494	62	1	p.	p.	NOUN
ejpam-5494	62	2	pue	pue	PROPN
ejpam-5494	62	3	-	-	PUNCT
ejpam-5494	62	4	on	on	ADP
ejpam-5494	62	5	/	/	SYM
ejpam-5494	62	6	eur	eur	NOUN
ejpam-5494	62	7	.	.	PUNCT
ejpam-5494	63	1	j.	j.	PROPN
ejpam-5494	63	2	pure	pure	PROPN
ejpam-5494	63	3	appl	appl	PROPN
ejpam-5494	63	4	.	.	PROPN
ejpam-5494	63	5	math	math	PROPN
ejpam-5494	63	6	,	,	PUNCT
ejpam-5494	63	7	17	17	NUM
ejpam-5494	63	8	(	(	PUNCT
ejpam-5494	63	9	4	4	NUM
ejpam-5494	63	10	)	)	PUNCT
ejpam-5494	63	11	(	(	PUNCT
ejpam-5494	63	12	2024	2024	NUM
ejpam-5494	63	13	)	)	PUNCT
ejpam-5494	63	14	,	,	PUNCT
ejpam-5494	63	15	3826	3826	NUM
ejpam-5494	63	16	-	-	SYM
ejpam-5494	63	17	3846	3846	NUM
ejpam-5494	63	18	3829	3829	NUM
ejpam-5494	63	19	definition	definition	NOUN
ejpam-5494	63	20	3	3	NUM
ejpam-5494	63	21	.	.	PUNCT
ejpam-5494	64	1	[	[	X
ejpam-5494	64	2	7	7	X
ejpam-5494	64	3	]	]	X
ejpam-5494	64	4	the	the	DET
ejpam-5494	64	5	fractional	fractional	ADJ
ejpam-5494	64	6	derivative	derivative	NOUN
ejpam-5494	64	7	of	of	ADP
ejpam-5494	64	8	order	order	NOUN
ejpam-5494	64	9	γ	γ	X
ejpam-5494	64	10	>	>	X
ejpam-5494	64	11	0	0	NUM
ejpam-5494	64	12	in	in	ADP
ejpam-5494	64	13	the	the	DET
ejpam-5494	64	14	caputo	caputo	PROPN
ejpam-5494	64	15	sense	sense	NOUN
ejpam-5494	64	16	is	be	AUX
ejpam-5494	64	17	stated	state	VERB
ejpam-5494	64	18	as	as	ADP
ejpam-5494	64	19	dγ	dγ	PROPN
ejpam-5494	64	20	t	t	PROPN
ejpam-5494	64	21	u(x	u(x	PROPN
ejpam-5494	64	22	,	,	PUNCT
ejpam-5494	64	23	t	t	NOUN
ejpam-5494	64	24	)	)	PUNCT
ejpam-5494	64	25	=	=	SYM
ejpam-5494	65	1	∂γu(x	∂γu(x	NOUN
ejpam-5494	65	2	,	,	PUNCT
ejpam-5494	65	3	t	t	NOUN
ejpam-5494	65	4	)	)	PUNCT
ejpam-5494	65	5	∂tγ	∂tγ	PROPN
ejpam-5494	65	6	=	=	PUNCT
ejpam-5494	66	1			NOUN
ejpam-5494	66	2	1	1	NUM
ejpam-5494	66	3	γ(n−γ	γ(n−γ	NOUN
ejpam-5494	66	4	)	)	PUNCT
ejpam-5494	66	5	∫	∫	PROPN
ejpam-5494	67	1	t	t	PROPN
ejpam-5494	67	2	0	0	NUM
ejpam-5494	67	3	(	(	PUNCT
ejpam-5494	67	4	t−	t−	PROPN
ejpam-5494	67	5	τ)n−γ−1	τ)n−γ−1	PROPN
ejpam-5494	67	6	∂	∂	NUM
ejpam-5494	67	7	nu(x	nu(x	NOUN
ejpam-5494	67	8	,	,	PUNCT
ejpam-5494	67	9	τ	τ	NOUN
ejpam-5494	67	10	)	)	PUNCT
ejpam-5494	67	11	∂τn	∂τn	PROPN
ejpam-5494	67	12	dτ	dτ	PROPN
ejpam-5494	67	13	,	,	PUNCT
ejpam-5494	67	14	n−	n−	PROPN
ejpam-5494	67	15	1	1	NUM
ejpam-5494	67	16	<	<	X
ejpam-5494	67	17	γ	γ	X
ejpam-5494	67	18	<	<	X
ejpam-5494	67	19	n	n	PRON
ejpam-5494	67	20	∂nu(x	∂nu(x	NOUN
ejpam-5494	67	21	,	,	PUNCT
ejpam-5494	67	22	t	t	PROPN
ejpam-5494	67	23	)	)	PUNCT
ejpam-5494	67	24	∂tn	∂tn	PROPN
ejpam-5494	67	25	,	,	PUNCT
ejpam-5494	67	26	γ	γ	X
ejpam-5494	67	27	=	=	SYM
ejpam-5494	67	28	n	n	CCONJ
ejpam-5494	67	29	∈	∈	PROPN
ejpam-5494	67	30	n.	n.	NOUN
ejpam-5494	67	31	definition	definition	NOUN
ejpam-5494	67	32	4	4	NUM
ejpam-5494	67	33	.	.	PUNCT
ejpam-5494	68	1	[	[	X
ejpam-5494	68	2	17	17	NUM
ejpam-5494	68	3	]	]	PUNCT
ejpam-5494	68	4	the	the	DET
ejpam-5494	68	5	mittag	mittag	ADJ
ejpam-5494	68	6	-	-	PUNCT
ejpam-5494	68	7	leffler	leffler	NOUN
ejpam-5494	68	8	function	function	NOUN
ejpam-5494	68	9	ep(z	ep(z	PUNCT
ejpam-5494	68	10	)	)	PUNCT
ejpam-5494	68	11	with	with	ADP
ejpam-5494	68	12	p	p	PROPN
ejpam-5494	68	13	>	>	X
ejpam-5494	68	14	0	0	NUM
ejpam-5494	68	15	is	be	AUX
ejpam-5494	68	16	defined	define	VERB
ejpam-5494	68	17	as	as	ADP
ejpam-5494	68	18	ep(z	ep(z	PUNCT
ejpam-5494	68	19	)	)	PUNCT
ejpam-5494	68	20	=	=	PUNCT
ejpam-5494	69	1	∞∑	∞∑	NUM
ejpam-5494	69	2	n=0	n=0	NUM
ejpam-5494	69	3	zn	zn	X
ejpam-5494	69	4	γ(pn+	γ(pn+	PROPN
ejpam-5494	69	5	1	1	NUM
ejpam-5494	69	6	)	)	PUNCT
ejpam-5494	69	7	.	.	PUNCT
ejpam-5494	70	1	2.2	2.2	NUM
ejpam-5494	70	2	.	.	PUNCT
ejpam-5494	71	1	the	the	DET
ejpam-5494	71	2	sadik	sadik	PROPN
ejpam-5494	71	3	transform	transform	VERB
ejpam-5494	71	4	definition	definition	NOUN
ejpam-5494	71	5	5	5	NUM
ejpam-5494	71	6	.	.	PUNCT
ejpam-5494	72	1	[	[	X
ejpam-5494	72	2	27	27	NUM
ejpam-5494	72	3	]	]	X
ejpam-5494	72	4	if	if	SCONJ
ejpam-5494	72	5	f(t	f(t	NOUN
ejpam-5494	72	6	)	)	PUNCT
ejpam-5494	72	7	is	be	AUX
ejpam-5494	72	8	piecewise	piecewise	NOUN
ejpam-5494	72	9	continuous	continuous	ADJ
ejpam-5494	72	10	function	function	NOUN
ejpam-5494	72	11	on	on	ADP
ejpam-5494	72	12	the	the	DET
ejpam-5494	72	13	interval	interval	NOUN
ejpam-5494	72	14	0	0	NUM
ejpam-5494	72	15	⩽	⩽	PROPN
ejpam-5494	72	16	t	t	PROPN
ejpam-5494	72	17	⩽	⩽	NOUN
ejpam-5494	72	18	a	a	PRON
ejpam-5494	72	19	for	for	ADP
ejpam-5494	72	20	any	any	DET
ejpam-5494	72	21	a	a	DET
ejpam-5494	72	22	>	>	X
ejpam-5494	72	23	0	0	PUNCT
ejpam-5494	72	24	and	and	CCONJ
ejpam-5494	72	25	|f(t)|	|f(t)|	PROPN
ejpam-5494	72	26	⩽	⩽	ADJ
ejpam-5494	72	27	kebt	kebt	PROPN
ejpam-5494	72	28	when	when	SCONJ
ejpam-5494	72	29	t	t	PROPN
ejpam-5494	72	30	⩾	⩾	PROPN
ejpam-5494	72	31	m	m	PROPN
ejpam-5494	72	32	,	,	PUNCT
ejpam-5494	72	33	for	for	ADP
ejpam-5494	72	34	any	any	DET
ejpam-5494	72	35	real	real	ADJ
ejpam-5494	72	36	constant	constant	ADJ
ejpam-5494	72	37	b	b	NOUN
ejpam-5494	72	38	and	and	CCONJ
ejpam-5494	72	39	some	some	DET
ejpam-5494	72	40	positive	positive	ADJ
ejpam-5494	72	41	constant	constant	ADJ
ejpam-5494	72	42	k	k	PROPN
ejpam-5494	72	43	and	and	CCONJ
ejpam-5494	72	44	m	m	PROPN
ejpam-5494	72	45	.	.	PUNCT
ejpam-5494	73	1	then	then	ADV
ejpam-5494	73	2	sadik	sadik	PROPN
ejpam-5494	73	3	transform	transform	NOUN
ejpam-5494	73	4	of	of	ADP
ejpam-5494	73	5	f(t	f(t	PROPN
ejpam-5494	73	6	)	)	PUNCT
ejpam-5494	73	7	is	be	AUX
ejpam-5494	73	8	defined	define	VERB
ejpam-5494	73	9	by	by	ADP
ejpam-5494	73	10	s	s	PRON
ejpam-5494	73	11	[	[	X
ejpam-5494	73	12	f(t	f(t	NOUN
ejpam-5494	73	13	)	)	PUNCT
ejpam-5494	73	14	]	]	PUNCT
ejpam-5494	74	1	=	=	PUNCT
ejpam-5494	74	2	1	1	NUM
ejpam-5494	74	3	vβ	vβ	ADP
ejpam-5494	74	4	∫	∫	PROPN
ejpam-5494	74	5	∞	∞	NOUN
ejpam-5494	74	6	0	0	NUM
ejpam-5494	74	7	f(t)e−tvαdt	f(t)e−tvαdt	PROPN
ejpam-5494	75	1	=	=	SYM
ejpam-5494	75	2	f	f	PROPN
ejpam-5494	75	3	(	(	PUNCT
ejpam-5494	75	4	vα	vα	PROPN
ejpam-5494	75	5	,	,	PUNCT
ejpam-5494	75	6	β	β	NOUN
ejpam-5494	75	7	)	)	PUNCT
ejpam-5494	75	8	(	(	PUNCT
ejpam-5494	75	9	4	4	X
ejpam-5494	75	10	)	)	PUNCT
ejpam-5494	75	11	where	where	SCONJ
ejpam-5494	75	12	v	v	NOUN
ejpam-5494	75	13	is	be	AUX
ejpam-5494	75	14	complex	complex	ADJ
ejpam-5494	75	15	variable	variable	NOUN
ejpam-5494	75	16	,	,	PUNCT
ejpam-5494	75	17	α	α	PROPN
ejpam-5494	75	18	is	be	AUX
ejpam-5494	75	19	any	any	DET
ejpam-5494	75	20	non	non	ADJ
ejpam-5494	75	21	zero	zero	NUM
ejpam-5494	75	22	real	real	ADJ
ejpam-5494	75	23	number	number	NOUN
ejpam-5494	75	24	,	,	PUNCT
ejpam-5494	75	25	and	and	CCONJ
ejpam-5494	75	26	β	β	X
ejpam-5494	75	27	is	be	AUX
ejpam-5494	75	28	any	any	DET
ejpam-5494	75	29	real	real	ADJ
ejpam-5494	75	30	number	number	NOUN
ejpam-5494	75	31	.	.	PUNCT
ejpam-5494	76	1	here	here	ADV
ejpam-5494	76	2	s	s	VERB
ejpam-5494	76	3	is	be	AUX
ejpam-5494	76	4	called	call	VERB
ejpam-5494	76	5	the	the	DET
ejpam-5494	76	6	sadik	sadik	PROPN
ejpam-5494	76	7	transform	transform	NOUN
ejpam-5494	76	8	operator	operator	NOUN
ejpam-5494	76	9	.	.	PUNCT
ejpam-5494	77	1	remark	remark	PROPN
ejpam-5494	77	2	1	1	NUM
ejpam-5494	77	3	.	.	PUNCT
ejpam-5494	78	1	the	the	DET
ejpam-5494	78	2	sadik	sadik	PROPN
ejpam-5494	78	3	transform	transform	NOUN
ejpam-5494	78	4	can	can	AUX
ejpam-5494	78	5	be	be	AUX
ejpam-5494	78	6	evolved	evolve	VERB
ejpam-5494	78	7	to	to	ADP
ejpam-5494	78	8	the	the	DET
ejpam-5494	78	9	other	other	ADJ
ejpam-5494	78	10	intrgral	intrgral	ADJ
ejpam-5494	78	11	transform	transform	NOUN
ejpam-5494	78	12	by	by	ADP
ejpam-5494	78	13	assigning	assign	VERB
ejpam-5494	78	14	the	the	DET
ejpam-5494	78	15	parameter	parameter	NOUN
ejpam-5494	78	16	α	α	PROPN
ejpam-5494	78	17	and	and	CCONJ
ejpam-5494	78	18	β	β	PROPN
ejpam-5494	78	19	as	as	SCONJ
ejpam-5494	78	20	follows	follow	VERB
ejpam-5494	78	21	:	:	PUNCT
ejpam-5494	78	22	α	α	X
ejpam-5494	78	23	=	=	SYM
ejpam-5494	78	24	1	1	NUM
ejpam-5494	78	25	,	,	PUNCT
ejpam-5494	78	26	β	β	X
ejpam-5494	78	27	=	=	SYM
ejpam-5494	78	28	0	0	PUNCT
ejpam-5494	79	1	(	(	PUNCT
ejpam-5494	79	2	laplace	laplace	NOUN
ejpam-5494	79	3	transform	transform	NOUN
ejpam-5494	79	4	)	)	PUNCT
ejpam-5494	79	5	,	,	PUNCT
ejpam-5494	79	6	α	α	X
ejpam-5494	79	7	=	=	SYM
ejpam-5494	79	8	1	1	NUM
ejpam-5494	79	9	,	,	PUNCT
ejpam-5494	79	10	β	β	X
ejpam-5494	79	11	=	=	SYM
ejpam-5494	79	12	1	1	NUM
ejpam-5494	79	13	(	(	PUNCT
ejpam-5494	79	14	aboodh	aboodh	NOUN
ejpam-5494	79	15	transform	transform	NOUN
ejpam-5494	79	16	)	)	PUNCT
ejpam-5494	79	17	,	,	PUNCT
ejpam-5494	79	18	α	α	X
ejpam-5494	79	19	=	=	SYM
ejpam-5494	79	20	1	1	NUM
ejpam-5494	79	21	,	,	PUNCT
ejpam-5494	79	22	β	β	NOUN
ejpam-5494	79	23	=	=	SYM
ejpam-5494	79	24	−1	−1	NOUN
ejpam-5494	79	25	(	(	PUNCT
ejpam-5494	79	26	laplace	laplace	NOUN
ejpam-5494	79	27	–	–	PUNCT
ejpam-5494	79	28	carson	carson	PROPN
ejpam-5494	79	29	transform	transform	NOUN
ejpam-5494	79	30	)	)	PUNCT
ejpam-5494	79	31	,	,	PUNCT
ejpam-5494	79	32	α	α	PROPN
ejpam-5494	79	33	=	=	SYM
ejpam-5494	79	34	−1	−1	NOUN
ejpam-5494	79	35	,	,	PUNCT
ejpam-5494	79	36	β	β	X
ejpam-5494	79	37	=	=	SYM
ejpam-5494	79	38	0	0	PUNCT
ejpam-5494	80	1	(	(	PUNCT
ejpam-5494	80	2	kamal	kamal	PROPN
ejpam-5494	80	3	transformx	transformx	PROPN
ejpam-5494	80	4	,	,	PUNCT
ejpam-5494	80	5	α	α	PROPN
ejpam-5494	80	6	=	=	SYM
ejpam-5494	80	7	−1	−1	NOUN
ejpam-5494	80	8	,	,	PUNCT
ejpam-5494	80	9	β	β	X
ejpam-5494	80	10	=	=	SYM
ejpam-5494	80	11	1	1	NUM
ejpam-5494	80	12	(	(	PUNCT
ejpam-5494	80	13	sumudu	sumudu	NOUN
ejpam-5494	80	14	transform	transform	NOUN
ejpam-5494	80	15	)	)	PUNCT
ejpam-5494	80	16	,	,	PUNCT
ejpam-5494	80	17	α	α	NOUN
ejpam-5494	80	18	=	=	SYM
ejpam-5494	80	19	−1	−1	NOUN
ejpam-5494	80	20	,	,	PUNCT
ejpam-5494	80	21	β	β	X
ejpam-5494	80	22	=	=	SYM
ejpam-5494	80	23	−1	−1	NOUN
ejpam-5494	80	24	(	(	PUNCT
ejpam-5494	80	25	elzaki	elzaki	NOUN
ejpam-5494	80	26	transform	transform	NOUN
ejpam-5494	80	27	)	)	PUNCT
ejpam-5494	80	28	,	,	PUNCT
ejpam-5494	80	29	α	α	NOUN
ejpam-5494	80	30	=	=	SYM
ejpam-5494	80	31	−2	−2	NOUN
ejpam-5494	80	32	,	,	PUNCT
ejpam-5494	80	33	β	β	X
ejpam-5494	80	34	=	=	SYM
ejpam-5494	80	35	1	1	NUM
ejpam-5494	80	36	(	(	PUNCT
ejpam-5494	80	37	tarig	tarig	NOUN
ejpam-5494	80	38	transform	transform	NOUN
ejpam-5494	80	39	)	)	PUNCT
ejpam-5494	80	40	.	.	PUNCT
ejpam-5494	81	1	remark	remark	PROPN
ejpam-5494	81	2	2	2	NUM
ejpam-5494	81	3	.	.	PUNCT
ejpam-5494	82	1	the	the	DET
ejpam-5494	82	2	basic	basic	ADJ
ejpam-5494	82	3	property	property	NOUN
ejpam-5494	82	4	of	of	ADP
ejpam-5494	82	5	sadik	sadik	PROPN
ejpam-5494	82	6	transform	transform	NOUN
ejpam-5494	82	7	and	and	CCONJ
ejpam-5494	82	8	its	its	PRON
ejpam-5494	82	9	transform	transform	NOUN
ejpam-5494	82	10	of	of	ADP
ejpam-5494	82	11	elemetary	elemetary	ADJ
ejpam-5494	82	12	functions	function	NOUN
ejpam-5494	82	13	are	be	AUX
ejpam-5494	82	14	shown	show	VERB
ejpam-5494	82	15	in	in	ADP
ejpam-5494	82	16	[	[	X
ejpam-5494	82	17	27	27	NUM
ejpam-5494	82	18	]	]	PUNCT
ejpam-5494	82	19	.	.	PUNCT
ejpam-5494	83	1	theorem	theorem	NOUN
ejpam-5494	83	2	1	1	NUM
ejpam-5494	83	3	.	.	PUNCT
ejpam-5494	84	1	[	[	X
ejpam-5494	84	2	25	25	NUM
ejpam-5494	84	3	]	]	PUNCT
ejpam-5494	84	4	let	let	VERB
ejpam-5494	84	5	f	f	PROPN
ejpam-5494	84	6	(	(	PUNCT
ejpam-5494	84	7	vα	vα	PROPN
ejpam-5494	84	8	,	,	PUNCT
ejpam-5494	84	9	β	β	NOUN
ejpam-5494	84	10	)	)	PUNCT
ejpam-5494	84	11	denote	denote	VERB
ejpam-5494	84	12	the	the	DET
ejpam-5494	84	13	sadik	sadik	PROPN
ejpam-5494	84	14	transform	transform	NOUN
ejpam-5494	84	15	of	of	ADP
ejpam-5494	84	16	f(t	f(t	PROPN
ejpam-5494	84	17	)	)	PUNCT
ejpam-5494	84	18	and	and	CCONJ
ejpam-5494	84	19	f	f	PROPN
ejpam-5494	84	20	′(t	′(t	PROPN
ejpam-5494	84	21	)	)	PUNCT
ejpam-5494	84	22	,	,	PUNCT
ejpam-5494	84	23	f	f	PROPN
ejpam-5494	84	24	′′(t	′′(t	PROPN
ejpam-5494	84	25	)	)	PUNCT
ejpam-5494	84	26	,	,	PUNCT
ejpam-5494	84	27	f	f	PROPN
ejpam-5494	84	28	′′′(t	′′′(t	PROPN
ejpam-5494	84	29	)	)	PUNCT
ejpam-5494	84	30	,	,	PUNCT
ejpam-5494	84	31	.	.	PUNCT
ejpam-5494	84	32	.	.	PUNCT
ejpam-5494	85	1	.	.	PUNCT
ejpam-5494	86	1	,	,	PUNCT
ejpam-5494	86	2	f	f	PROPN
ejpam-5494	86	3	(	(	PUNCT
ejpam-5494	86	4	n−1)(t	n−1)(t	PROPN
ejpam-5494	86	5	)	)	PUNCT
ejpam-5494	86	6	are	be	AUX
ejpam-5494	86	7	continuous	continuous	ADJ
ejpam-5494	86	8	on	on	ADP
ejpam-5494	86	9	[	[	X
ejpam-5494	86	10	0,∞.	0,∞.	NUM
ejpam-5494	86	11	)	)	PUNCT
ejpam-5494	86	12	then	then	ADV
ejpam-5494	86	13	the	the	DET
ejpam-5494	86	14	sadik	sadik	PROPN
ejpam-5494	86	15	transform	transform	NOUN
ejpam-5494	86	16	of	of	ADP
ejpam-5494	86	17	f	f	PROPN
ejpam-5494	86	18	(	(	PUNCT
ejpam-5494	86	19	n)(t	n)(t	PROPN
ejpam-5494	86	20	)	)	PUNCT
ejpam-5494	86	21	is	be	AUX
ejpam-5494	86	22	s	s	PART
ejpam-5494	86	23	[	[	PUNCT
ejpam-5494	86	24	f	f	X
ejpam-5494	86	25	(	(	PUNCT
ejpam-5494	86	26	n)(t	n)(t	PROPN
ejpam-5494	86	27	)	)	PUNCT
ejpam-5494	86	28	]	]	PUNCT
ejpam-5494	87	1	=	=	PUNCT
ejpam-5494	87	2	vnαf	vnαf	NOUN
ejpam-5494	87	3	(	(	PUNCT
ejpam-5494	87	4	vα	vα	INTJ
ejpam-5494	87	5	,	,	PUNCT
ejpam-5494	87	6	β)−	β)−	ADJ
ejpam-5494	87	7	n−1∑	n−1∑	NUM
ejpam-5494	87	8	k=0	k=0	PROPN
ejpam-5494	87	9	vkα−βf	vkα−βf	NOUN
ejpam-5494	87	10	(	(	PUNCT
ejpam-5494	87	11	n−1−k)(0	n−1−k)(0	PROPN
ejpam-5494	87	12	)	)	PUNCT
ejpam-5494	87	13	.	.	PUNCT
ejpam-5494	88	1	(	(	PUNCT
ejpam-5494	88	2	5	5	X
ejpam-5494	88	3	)	)	PUNCT
ejpam-5494	88	4	theorem	theorem	NOUN
ejpam-5494	88	5	2	2	NUM
ejpam-5494	88	6	.	.	PUNCT
ejpam-5494	89	1	[	[	X
ejpam-5494	89	2	25	25	NUM
ejpam-5494	89	3	]	]	PUNCT
ejpam-5494	89	4	let	let	VERB
ejpam-5494	89	5	n	n	INTJ
ejpam-5494	89	6	−	−	PROPN
ejpam-5494	89	7	1	1	NUM
ejpam-5494	89	8	<	<	X
ejpam-5494	89	9	γ	γ	X
ejpam-5494	89	10	<	<	X
ejpam-5494	89	11	n	n	NUM
ejpam-5494	89	12	,	,	PUNCT
ejpam-5494	89	13	(	(	PUNCT
ejpam-5494	89	14	n	n	NOUN
ejpam-5494	89	15	=	=	PUNCT
ejpam-5494	90	1	[	[	X
ejpam-5494	90	2	γ	γ	X
ejpam-5494	90	3	]	]	X
ejpam-5494	90	4	+	+	NUM
ejpam-5494	90	5	1	1	NUM
ejpam-5494	90	6	)	)	PUNCT
ejpam-5494	90	7	and	and	CCONJ
ejpam-5494	90	8	f(t	f(t	NOUN
ejpam-5494	90	9	)	)	PUNCT
ejpam-5494	90	10	,	,	PUNCT
ejpam-5494	90	11	f	f	PROPN
ejpam-5494	90	12	′(t	′(t	PROPN
ejpam-5494	90	13	)	)	PUNCT
ejpam-5494	90	14	,	,	PUNCT
ejpam-5494	90	15	.	.	PUNCT
ejpam-5494	90	16	.	.	PUNCT
ejpam-5494	91	1	.	.	PUNCT
ejpam-5494	92	1	,	,	PUNCT
ejpam-5494	92	2	f	f	PROPN
ejpam-5494	92	3	(	(	PUNCT
ejpam-5494	92	4	n−1)(t	n−1)(t	PROPN
ejpam-5494	92	5	)	)	PUNCT
ejpam-5494	92	6	are	be	AUX
ejpam-5494	92	7	continuous	continuous	ADJ
ejpam-5494	92	8	on	on	ADP
ejpam-5494	92	9	[	[	X
ejpam-5494	92	10	0,∞	0,∞	NOUN
ejpam-5494	92	11	)	)	PUNCT
ejpam-5494	92	12	and	and	CCONJ
ejpam-5494	92	13	of	of	ADP
ejpam-5494	92	14	exponential	exponential	ADJ
ejpam-5494	92	15	order	order	NOUN
ejpam-5494	92	16	,	,	PUNCT
ejpam-5494	92	17	while	while	SCONJ
ejpam-5494	92	18	dγf(t	dγf(t	NOUN
ejpam-5494	92	19	)	)	PUNCT
ejpam-5494	92	20	is	be	AUX
ejpam-5494	92	21	piecewise	piecewise	NOUN
ejpam-5494	92	22	continuous	continuous	ADJ
ejpam-5494	92	23	on	on	ADP
ejpam-5494	92	24	[	[	X
ejpam-5494	92	25	0,∞	0,∞	NOUN
ejpam-5494	92	26	)	)	PUNCT
ejpam-5494	92	27	.	.	PUNCT
ejpam-5494	93	1	then	then	ADV
ejpam-5494	93	2	sadik	sadik	PROPN
ejpam-5494	93	3	transform	transform	NOUN
ejpam-5494	93	4	of	of	ADP
ejpam-5494	93	5	caputo	caputo	PROPN
ejpam-5494	93	6	fractional	fractional	PROPN
ejpam-5494	93	7	derivative	derivative	NOUN
ejpam-5494	93	8	of	of	ADP
ejpam-5494	93	9	order	order	NOUN
ejpam-5494	93	10	γ	γ	NOUN
ejpam-5494	93	11	of	of	ADP
ejpam-5494	93	12	function	function	NOUN
ejpam-5494	93	13	f	f	PROPN
ejpam-5494	93	14	is	be	AUX
ejpam-5494	93	15	given	give	VERB
ejpam-5494	93	16	by	by	ADP
ejpam-5494	93	17	s[dγf(t	s[dγf(t	NOUN
ejpam-5494	93	18	)	)	PUNCT
ejpam-5494	93	19	]	]	PUNCT
ejpam-5494	94	1	=	=	SYM
ejpam-5494	94	2	vγαf	vγαf	NOUN
ejpam-5494	94	3	(	(	PUNCT
ejpam-5494	94	4	vα	vα	INTJ
ejpam-5494	94	5	,	,	PUNCT
ejpam-5494	94	6	β)−	β)−	ADJ
ejpam-5494	94	7	n−1∑	n−1∑	NUM
ejpam-5494	94	8	k=0	k=0	PROPN
ejpam-5494	94	9	v(γ−n+k)α−βf	v(γ−n+k)α−βf	NOUN
ejpam-5494	94	10	(	(	PUNCT
ejpam-5494	94	11	n−1−k)(0	n−1−k)(0	NOUN
ejpam-5494	94	12	+	+	NOUN
ejpam-5494	94	13	)	)	PUNCT
ejpam-5494	94	14	.	.	PUNCT
ejpam-5494	95	1	p.	p.	NOUN
ejpam-5494	95	2	pue	pue	NOUN
ejpam-5494	95	3	-	-	PUNCT
ejpam-5494	95	4	on	on	ADP
ejpam-5494	95	5	/	/	SYM
ejpam-5494	95	6	eur	eur	NOUN
ejpam-5494	95	7	.	.	PUNCT
ejpam-5494	96	1	j.	j.	PROPN
ejpam-5494	96	2	pure	pure	PROPN
ejpam-5494	96	3	appl	appl	PROPN
ejpam-5494	96	4	.	.	PROPN
ejpam-5494	96	5	math	math	PROPN
ejpam-5494	96	6	,	,	PUNCT
ejpam-5494	96	7	17	17	NUM
ejpam-5494	96	8	(	(	PUNCT
ejpam-5494	96	9	4	4	NUM
ejpam-5494	96	10	)	)	PUNCT
ejpam-5494	96	11	(	(	PUNCT
ejpam-5494	96	12	2024	2024	NUM
ejpam-5494	96	13	)	)	PUNCT
ejpam-5494	96	14	,	,	PUNCT
ejpam-5494	96	15	3826	3826	NUM
ejpam-5494	96	16	-	-	SYM
ejpam-5494	96	17	3846	3846	NUM
ejpam-5494	96	18	3830	3830	NUM
ejpam-5494	96	19	2.3	2.3	NUM
ejpam-5494	96	20	.	.	PUNCT
ejpam-5494	97	1	the	the	DET
ejpam-5494	97	2	residual	residual	ADJ
ejpam-5494	97	3	power	power	NOUN
ejpam-5494	97	4	series	series	PROPN
ejpam-5494	97	5	method	method	PROPN
ejpam-5494	97	6	definition	definition	NOUN
ejpam-5494	97	7	6	6	NUM
ejpam-5494	97	8	.	.	PUNCT
ejpam-5494	98	1	[	[	X
ejpam-5494	98	2	10	10	NUM
ejpam-5494	98	3	,	,	PUNCT
ejpam-5494	98	4	11	11	NUM
ejpam-5494	98	5	]	]	PUNCT
ejpam-5494	98	6	if	if	SCONJ
ejpam-5494	98	7	n	n	PRON
ejpam-5494	98	8	∈	∈	PROPN
ejpam-5494	98	9	n	n	CCONJ
ejpam-5494	98	10	where	where	SCONJ
ejpam-5494	98	11	n	n	ADV
ejpam-5494	98	12	−	−	PROPN
ejpam-5494	98	13	1	1	NUM
ejpam-5494	98	14	<	<	X
ejpam-5494	98	15	γ	γ	X
ejpam-5494	98	16	⩽	⩽	PROPN
ejpam-5494	98	17	n.	n.	PROPN
ejpam-5494	98	18	a	a	DET
ejpam-5494	98	19	power	power	NOUN
ejpam-5494	98	20	series	series	NOUN
ejpam-5494	98	21	expansion	expansion	NOUN
ejpam-5494	98	22	of	of	ADP
ejpam-5494	98	23	the	the	DET
ejpam-5494	98	24	form	form	NOUN
ejpam-5494	98	25	∞∑	∞∑	PROPN
ejpam-5494	98	26	n=0	n=0	NUM
ejpam-5494	98	27	an(t−	an(t−	PRON
ejpam-5494	98	28	t0	t0	PROPN
ejpam-5494	98	29	)	)	PUNCT
ejpam-5494	98	30	nγ	nγ	NOUN
ejpam-5494	98	31	=	=	PROPN
ejpam-5494	98	32	a0	a0	PROPN
ejpam-5494	98	33	+	+	CCONJ
ejpam-5494	98	34	a1(t−	a1(t−	NOUN
ejpam-5494	98	35	t0	t0	NOUN
ejpam-5494	98	36	)	)	PUNCT
ejpam-5494	98	37	γ	γ	PROPN
ejpam-5494	98	38	+	+	CCONJ
ejpam-5494	98	39	a2(t−	a2(t−	NOUN
ejpam-5494	98	40	t0	t0	NOUN
ejpam-5494	98	41	)	)	PUNCT
ejpam-5494	98	42	2γ	2γ	NOUN
ejpam-5494	98	43	+	+	X
ejpam-5494	98	44	.	.	PUNCT
ejpam-5494	98	45	.	.	PUNCT
ejpam-5494	98	46	.	.	PUNCT
ejpam-5494	99	1	,	,	PUNCT
ejpam-5494	99	2	t	t	PROPN
ejpam-5494	99	3	⩾	⩾	PROPN
ejpam-5494	99	4	t0	t0	PROPN
ejpam-5494	99	5	is	be	AUX
ejpam-5494	99	6	called	call	VERB
ejpam-5494	99	7	fractional	fractional	ADJ
ejpam-5494	99	8	power	power	NOUN
ejpam-5494	99	9	series	series	NOUN
ejpam-5494	99	10	about	about	ADP
ejpam-5494	99	11	t0	t0	PROPN
ejpam-5494	99	12	.	.	PUNCT
ejpam-5494	100	1	theorem	theorem	NOUN
ejpam-5494	100	2	3	3	NUM
ejpam-5494	100	3	.	.	PUNCT
ejpam-5494	101	1	[	[	X
ejpam-5494	101	2	10	10	NUM
ejpam-5494	101	3	,	,	PUNCT
ejpam-5494	101	4	11	11	NUM
ejpam-5494	101	5	]	]	PUNCT
ejpam-5494	101	6	suppose	suppose	VERB
ejpam-5494	101	7	that	that	SCONJ
ejpam-5494	101	8	u(t	u(t	NOUN
ejpam-5494	101	9	)	)	PUNCT
ejpam-5494	101	10	has	have	VERB
ejpam-5494	101	11	a	a	DET
ejpam-5494	101	12	fractional	fractional	ADJ
ejpam-5494	101	13	power	power	NOUN
ejpam-5494	101	14	series	series	NOUN
ejpam-5494	101	15	representation	representation	NOUN
ejpam-5494	101	16	at	at	ADP
ejpam-5494	101	17	t	t	PROPN
ejpam-5494	101	18	=	=	SYM
ejpam-5494	101	19	t0	t0	PROPN
ejpam-5494	101	20	of	of	ADP
ejpam-5494	101	21	the	the	DET
ejpam-5494	101	22	form	form	NOUN
ejpam-5494	101	23	u(t	u(t	NOUN
ejpam-5494	101	24	)	)	PUNCT
ejpam-5494	101	25	=	=	X
ejpam-5494	102	1	∞∑	∞∑	NUM
ejpam-5494	102	2	n=0	n=0	NUM
ejpam-5494	102	3	an(t−	an(t−	PROPN
ejpam-5494	102	4	t0	t0	PROPN
ejpam-5494	102	5	)	)	PUNCT
ejpam-5494	102	6	nγ	nγ	NOUN
ejpam-5494	102	7	,	,	PUNCT
ejpam-5494	102	8	0	0	NUM
ejpam-5494	102	9	⩽	⩽	NOUN
ejpam-5494	102	10	m−	m−	PROPN
ejpam-5494	102	11	1	1	NUM
ejpam-5494	102	12	<	<	X
ejpam-5494	102	13	γ	γ	X
ejpam-5494	102	14	⩽	⩽	PROPN
ejpam-5494	102	15	m	m	PROPN
ejpam-5494	102	16	,	,	PUNCT
ejpam-5494	102	17	t0	t0	PROPN
ejpam-5494	102	18	⩽	⩽	PROPN
ejpam-5494	102	19	t	t	PROPN
ejpam-5494	102	20	<	<	X
ejpam-5494	102	21	t0	t0	PROPN
ejpam-5494	103	1	+	+	SYM
ejpam-5494	103	2	r.	r.	PROPN
ejpam-5494	103	3	if	if	SCONJ
ejpam-5494	103	4	u(t	u(t	NOUN
ejpam-5494	103	5	)	)	PUNCT
ejpam-5494	103	6	∈	∈	PROPN
ejpam-5494	103	7	c[t0	c[t0	NOUN
ejpam-5494	103	8	,	,	PUNCT
ejpam-5494	103	9	t0	t0	PROPN
ejpam-5494	103	10	+	+	NOUN
ejpam-5494	103	11	r	r	NOUN
ejpam-5494	103	12	)	)	PUNCT
ejpam-5494	103	13	and	and	CCONJ
ejpam-5494	103	14	dnγu(t	dnγu(t	PROPN
ejpam-5494	103	15	)	)	PUNCT
ejpam-5494	103	16	∈	∈	PROPN
ejpam-5494	103	17	c(t0	c(t0	NOUN
ejpam-5494	103	18	,	,	PUNCT
ejpam-5494	103	19	t0	t0	PROPN
ejpam-5494	104	1	+	+	NOUN
ejpam-5494	104	2	r	r	NOUN
ejpam-5494	104	3	)	)	PUNCT
ejpam-5494	104	4	,	,	PUNCT
ejpam-5494	104	5	n	n	NOUN
ejpam-5494	104	6	=	=	SYM
ejpam-5494	104	7	0	0	NUM
ejpam-5494	104	8	,	,	PUNCT
ejpam-5494	104	9	1	1	NUM
ejpam-5494	104	10	,	,	PUNCT
ejpam-5494	104	11	2	2	NUM
ejpam-5494	104	12	,	,	PUNCT
ejpam-5494	104	13	.	.	PUNCT
ejpam-5494	104	14	.	.	PUNCT
ejpam-5494	105	1	.	.	PUNCT
ejpam-5494	106	1	,	,	PUNCT
ejpam-5494	106	2	then	then	ADV
ejpam-5494	106	3	an	an	DET
ejpam-5494	106	4	=	=	SYM
ejpam-5494	106	5	dnγu(t	dnγu(t	PROPN
ejpam-5494	106	6	)	)	PUNCT
ejpam-5494	106	7	γ(nγ+1	γ(nγ+1	NUM
ejpam-5494	106	8	)	)	PUNCT
ejpam-5494	106	9	.	.	PUNCT
ejpam-5494	107	1	definition	definition	NOUN
ejpam-5494	107	2	7	7	NUM
ejpam-5494	107	3	.	.	PUNCT
ejpam-5494	108	1	[	[	X
ejpam-5494	108	2	10	10	NUM
ejpam-5494	108	3	,	,	PUNCT
ejpam-5494	108	4	11	11	NUM
ejpam-5494	108	5	]	]	PUNCT
ejpam-5494	108	6	a	a	DET
ejpam-5494	108	7	power	power	NOUN
ejpam-5494	108	8	series	series	NOUN
ejpam-5494	108	9	of	of	ADP
ejpam-5494	108	10	the	the	DET
ejpam-5494	108	11	form	form	NOUN
ejpam-5494	108	12	∞∑	∞∑	PROPN
ejpam-5494	108	13	n=0	n=0	NUM
ejpam-5494	108	14	fn(x)(t−	fn(x)(t−	NOUN
ejpam-5494	108	15	t0	t0	PROPN
ejpam-5494	108	16	)	)	PUNCT
ejpam-5494	108	17	nγ	nγ	NOUN
ejpam-5494	108	18	=	=	SYM
ejpam-5494	108	19	f0(x	f0(x	NOUN
ejpam-5494	108	20	)	)	PUNCT
ejpam-5494	108	21	+	+	NOUN
ejpam-5494	108	22	f1(x)(t−	f1(x)(t−	PROPN
ejpam-5494	108	23	t0	t0	NOUN
ejpam-5494	108	24	)	)	PUNCT
ejpam-5494	108	25	γ	γ	PROPN
ejpam-5494	108	26	+	+	CCONJ
ejpam-5494	108	27	f2(x)(t−	f2(x)(t−	PROPN
ejpam-5494	108	28	t0	t0	PROPN
ejpam-5494	108	29	)	)	PUNCT
ejpam-5494	108	30	2γ	2γ	NOUN
ejpam-5494	108	31	+	+	X
ejpam-5494	108	32	.	.	PUNCT
ejpam-5494	108	33	.	.	PUNCT
ejpam-5494	108	34	.	.	PUNCT
ejpam-5494	109	1	is	be	AUX
ejpam-5494	109	2	called	call	VERB
ejpam-5494	109	3	multiple	multiple	ADJ
ejpam-5494	109	4	fractional	fractional	ADJ
ejpam-5494	109	5	power	power	NOUN
ejpam-5494	109	6	series	series	NOUN
ejpam-5494	109	7	about	about	ADP
ejpam-5494	109	8	t	t	PROPN
ejpam-5494	109	9	=	=	SYM
ejpam-5494	109	10	t0	t0	PROPN
ejpam-5494	109	11	,	,	PUNCT
ejpam-5494	109	12	where	where	SCONJ
ejpam-5494	109	13	t	t	PROPN
ejpam-5494	109	14	is	be	AUX
ejpam-5494	109	15	a	a	DET
ejpam-5494	109	16	variable	variable	NOUN
ejpam-5494	109	17	and	and	CCONJ
ejpam-5494	109	18	fm	fm	PROPN
ejpam-5494	109	19	’s	’s	PART
ejpam-5494	109	20	are	be	AUX
ejpam-5494	109	21	functions	function	NOUN
ejpam-5494	109	22	of	of	ADP
ejpam-5494	109	23	x	x	PUNCT
ejpam-5494	109	24	called	call	VERB
ejpam-5494	109	25	the	the	DET
ejpam-5494	109	26	coefficients	coefficient	NOUN
ejpam-5494	109	27	of	of	ADP
ejpam-5494	109	28	the	the	DET
ejpam-5494	109	29	series	series	NOUN
ejpam-5494	109	30	.	.	PUNCT
ejpam-5494	110	1	theorem	theorem	VERB
ejpam-5494	110	2	4	4	NUM
ejpam-5494	110	3	.	.	PUNCT
ejpam-5494	111	1	[	[	X
ejpam-5494	111	2	10	10	NUM
ejpam-5494	111	3	,	,	PUNCT
ejpam-5494	111	4	11	11	NUM
ejpam-5494	111	5	]	]	PUNCT
ejpam-5494	111	6	suppose	suppose	VERB
ejpam-5494	111	7	that	that	SCONJ
ejpam-5494	111	8	u(x	u(x	PROPN
ejpam-5494	111	9	,	,	PUNCT
ejpam-5494	111	10	t	t	PROPN
ejpam-5494	111	11	)	)	PUNCT
ejpam-5494	111	12	has	have	VERB
ejpam-5494	111	13	a	a	DET
ejpam-5494	111	14	multiple	multiple	ADJ
ejpam-5494	111	15	fractional	fractional	ADJ
ejpam-5494	111	16	power	power	NOUN
ejpam-5494	111	17	series	series	NOUN
ejpam-5494	111	18	representation	representation	NOUN
ejpam-5494	111	19	at	at	ADP
ejpam-5494	111	20	t	t	PROPN
ejpam-5494	111	21	=	=	SYM
ejpam-5494	111	22	t0	t0	PROPN
ejpam-5494	111	23	of	of	ADP
ejpam-5494	111	24	the	the	DET
ejpam-5494	111	25	form	form	NOUN
ejpam-5494	111	26	u(x	u(x	NOUN
ejpam-5494	111	27	,	,	PUNCT
ejpam-5494	111	28	t	t	NOUN
ejpam-5494	111	29	)	)	PUNCT
ejpam-5494	111	30	=	=	PUNCT
ejpam-5494	112	1	∞∑	∞∑	PRON
ejpam-5494	112	2	n=0	n=0	NUM
ejpam-5494	112	3	un(x	un(x	NUM
ejpam-5494	112	4	,	,	PUNCT
ejpam-5494	112	5	t	t	PROPN
ejpam-5494	112	6	)	)	PUNCT
ejpam-5494	112	7	=	=	PUNCT
ejpam-5494	113	1	∞∑	∞∑	NUM
ejpam-5494	113	2	n=0	n=0	NUM
ejpam-5494	113	3	fn(x)(t−	fn(x)(t−	PROPN
ejpam-5494	113	4	t0	t0	PROPN
ejpam-5494	113	5	)	)	PUNCT
ejpam-5494	113	6	nγ	nγ	NOUN
ejpam-5494	113	7	,	,	PUNCT
ejpam-5494	113	8	0	0	NUM
ejpam-5494	113	9	⩽	⩽	NOUN
ejpam-5494	113	10	m	m	VERB
ejpam-5494	113	11	−	−	PROPN
ejpam-5494	113	12	1	1	NUM
ejpam-5494	113	13	<	<	X
ejpam-5494	113	14	γ	γ	X
ejpam-5494	113	15	⩽	⩽	PROPN
ejpam-5494	113	16	m	m	PROPN
ejpam-5494	113	17	,	,	PUNCT
ejpam-5494	113	18	x	x	SYM
ejpam-5494	113	19	∈	∈	PROPN
ejpam-5494	113	20	i	i	PRON
ejpam-5494	113	21	,	,	PUNCT
ejpam-5494	113	22	t0	t0	PROPN
ejpam-5494	113	23	⩽	⩽	PROPN
ejpam-5494	113	24	t	t	PROPN
ejpam-5494	113	25	<	<	X
ejpam-5494	113	26	t0	t0	PROPN
ejpam-5494	113	27	+	+	CCONJ
ejpam-5494	113	28	r.	r.	PROPN
ejpam-5494	113	29	if	if	SCONJ
ejpam-5494	113	30	dnγ	dnγ	PROPN
ejpam-5494	113	31	t	t	PROPN
ejpam-5494	113	32	u(x	u(x	PROPN
ejpam-5494	113	33	,	,	PUNCT
ejpam-5494	113	34	t	t	PROPN
ejpam-5494	113	35	)	)	PUNCT
ejpam-5494	113	36	,	,	PUNCT
ejpam-5494	113	37	n	n	NOUN
ejpam-5494	113	38	=	=	SYM
ejpam-5494	113	39	0	0	NUM
ejpam-5494	113	40	,	,	PUNCT
ejpam-5494	113	41	1	1	NUM
ejpam-5494	113	42	,	,	PUNCT
ejpam-5494	113	43	2	2	NUM
ejpam-5494	113	44	,	,	PUNCT
ejpam-5494	113	45	.	.	PUNCT
ejpam-5494	113	46	.	.	PUNCT
ejpam-5494	114	1	.	.	PUNCT
ejpam-5494	115	1	are	be	AUX
ejpam-5494	115	2	continuous	continuous	ADJ
ejpam-5494	115	3	on	on	ADP
ejpam-5494	115	4	i	i	PRON
ejpam-5494	115	5	×	×	PROPN
ejpam-5494	115	6	(	(	PUNCT
ejpam-5494	115	7	t0	t0	PROPN
ejpam-5494	115	8	,	,	PUNCT
ejpam-5494	115	9	t0	t0	PROPN
ejpam-5494	115	10	+	+	NOUN
ejpam-5494	115	11	r	r	NOUN
ejpam-5494	115	12	)	)	PUNCT
ejpam-5494	115	13	,	,	PUNCT
ejpam-5494	115	14	then	then	ADV
ejpam-5494	115	15	fn(x	fn(x	PRON
ejpam-5494	115	16	)	)	PUNCT
ejpam-5494	115	17	=	=	SYM
ejpam-5494	115	18	dnγ	dnγ	PROPN
ejpam-5494	115	19	t	t	PROPN
ejpam-5494	115	20	u(x	u(x	PROPN
ejpam-5494	115	21	,	,	PUNCT
ejpam-5494	115	22	t	t	NOUN
ejpam-5494	115	23	)	)	PUNCT
ejpam-5494	115	24	γ(nγ	γ(nγ	NOUN
ejpam-5494	115	25	+	+	CCONJ
ejpam-5494	115	26	1	1	NUM
ejpam-5494	115	27	)	)	PUNCT
ejpam-5494	115	28	,	,	PUNCT
ejpam-5494	115	29	n	n	NOUN
ejpam-5494	115	30	=	=	SYM
ejpam-5494	115	31	0	0	NUM
ejpam-5494	115	32	,	,	PUNCT
ejpam-5494	115	33	1	1	NUM
ejpam-5494	115	34	,	,	PUNCT
ejpam-5494	115	35	2	2	NUM
ejpam-5494	115	36	,	,	PUNCT
ejpam-5494	115	37	.	.	PUNCT
ejpam-5494	115	38	.	.	PUNCT
ejpam-5494	115	39	.	.	PUNCT
ejpam-5494	115	40	.	.	PUNCT
ejpam-5494	116	1	here	here	ADV
ejpam-5494	116	2	dnγ	dnγ	PROPN
ejpam-5494	116	3	t	t	PROPN
ejpam-5494	116	4	(	(	PUNCT
ejpam-5494	116	5	·	·	PUNCT
ejpam-5494	116	6	)	)	PUNCT
ejpam-5494	116	7	=	=	SYM
ejpam-5494	116	8	∂nγ	∂nγ	PROPN
ejpam-5494	116	9	∂tnγ	∂tnγ	NUM
ejpam-5494	116	10	(	(	PUNCT
ejpam-5494	116	11	·	·	PUNCT
ejpam-5494	116	12	)	)	PUNCT
ejpam-5494	117	1	=	=	PUNCT
ejpam-5494	117	2	∂γ	∂γ	PROPN
ejpam-5494	117	3	∂tγ	∂tγ	PROPN
ejpam-5494	117	4	(	(	PUNCT
ejpam-5494	117	5	∂γ	∂γ	NOUN
ejpam-5494	117	6	∂tγ	∂tγ	PROPN
ejpam-5494	117	7	(	(	PUNCT
ejpam-5494	117	8	.	.	PUNCT
ejpam-5494	117	9	.	.	PUNCT
ejpam-5494	117	10	.	.	PUNCT
ejpam-5494	118	1	(	(	PUNCT
ejpam-5494	118	2	∂γ	∂γ	NOUN
ejpam-5494	118	3	∂tγ	∂tγ	PROPN
ejpam-5494	118	4	(	(	PUNCT
ejpam-5494	118	5	·	·	PUNCT
ejpam-5494	118	6	)	)	PUNCT
ejpam-5494	118	7	)	)	PUNCT
ejpam-5494	118	8	)	)	PUNCT
ejpam-5494	118	9	)	)	PUNCT
ejpam-5494	119	1	(	(	PUNCT
ejpam-5494	119	2	n	n	CCONJ
ejpam-5494	119	3	−	−	PROPN
ejpam-5494	119	4	times	time	NOUN
ejpam-5494	119	5	)	)	PUNCT
ejpam-5494	119	6	,	,	PUNCT
ejpam-5494	119	7	and	and	CCONJ
ejpam-5494	119	8	r	r	NOUN
ejpam-5494	119	9	=	=	SYM
ejpam-5494	119	10	minc∈i	minc∈i	PROPN
ejpam-5494	119	11	rc	rc	PROPN
ejpam-5494	119	12	,	,	PUNCT
ejpam-5494	119	13	in	in	ADP
ejpam-5494	119	14	which	which	PRON
ejpam-5494	119	15	rc	rc	PROPN
ejpam-5494	119	16	is	be	AUX
ejpam-5494	119	17	the	the	DET
ejpam-5494	119	18	radius	radius	NOUN
ejpam-5494	119	19	of	of	ADP
ejpam-5494	119	20	convergence	convergence	NOUN
ejpam-5494	119	21	of	of	ADP
ejpam-5494	119	22	the	the	DET
ejpam-5494	119	23	fractional	fractional	ADJ
ejpam-5494	119	24	power	power	NOUN
ejpam-5494	119	25	series	series	NOUN
ejpam-5494	119	26	∑∞	∑∞	X
ejpam-5494	119	27	k=0	k=0	PUNCT
ejpam-5494	119	28	fn(c)(t−	fn(c)(t−	VERB
ejpam-5494	119	29	t0	t0	NUM
ejpam-5494	119	30	)	)	PUNCT
ejpam-5494	119	31	nγ	nγ	NOUN
ejpam-5494	119	32	.	.	PUNCT
ejpam-5494	120	1	according	accord	VERB
ejpam-5494	120	2	to	to	ADP
ejpam-5494	120	3	the	the	DET
ejpam-5494	120	4	convergence	convergence	NOUN
ejpam-5494	120	5	of	of	ADP
ejpam-5494	120	6	the	the	DET
ejpam-5494	120	7	classic	classic	ADJ
ejpam-5494	120	8	residual	residual	ADJ
ejpam-5494	120	9	power	power	NOUN
ejpam-5494	120	10	series	series	NOUN
ejpam-5494	120	11	method	method	NOUN
ejpam-5494	120	12	,	,	PUNCT
ejpam-5494	120	13	there	there	PRON
ejpam-5494	120	14	is	be	VERB
ejpam-5494	120	15	a	a	DET
ejpam-5494	120	16	real	real	ADJ
ejpam-5494	120	17	number	number	NOUN
ejpam-5494	120	18	0	0	NUM
ejpam-5494	120	19	<	<	X
ejpam-5494	120	20	λ	λ	X
ejpam-5494	120	21	<	<	X
ejpam-5494	120	22	1	1	NUM
ejpam-5494	120	23	,	,	PUNCT
ejpam-5494	120	24	such	such	ADJ
ejpam-5494	120	25	that	that	DET
ejpam-5494	120	26	||un+1(x	||un+1(x	NOUN
ejpam-5494	120	27	,	,	PUNCT
ejpam-5494	120	28	t)||	t)||	PROPN
ejpam-5494	120	29	⩽	⩽	PROPN
ejpam-5494	120	30	λ||un(x	λ||un(x	PROPN
ejpam-5494	120	31	,	,	PUNCT
ejpam-5494	120	32	t)||	t)||	PROPN
ejpam-5494	120	33	,	,	PUNCT
ejpam-5494	120	34	t	t	PROPN
ejpam-5494	120	35	∈	∈	PROPN
ejpam-5494	120	36	(	(	PUNCT
ejpam-5494	120	37	t0	t0	PROPN
ejpam-5494	120	38	,	,	PUNCT
ejpam-5494	120	39	t0	t0	PROPN
ejpam-5494	120	40	+	+	NOUN
ejpam-5494	120	41	r	r	NOUN
ejpam-5494	120	42	)	)	PUNCT
ejpam-5494	120	43	.	.	PUNCT
ejpam-5494	121	1	3	3	X
ejpam-5494	121	2	.	.	X
ejpam-5494	121	3	main	main	ADJ
ejpam-5494	121	4	results	result	NOUN
ejpam-5494	121	5	this	this	DET
ejpam-5494	121	6	section	section	NOUN
ejpam-5494	121	7	explains	explain	VERB
ejpam-5494	121	8	the	the	DET
ejpam-5494	121	9	sadik	sadik	PROPN
ejpam-5494	121	10	residual	residual	ADJ
ejpam-5494	121	11	power	power	NOUN
ejpam-5494	121	12	series	series	NOUN
ejpam-5494	121	13	method	method	NOUN
ejpam-5494	121	14	and	and	CCONJ
ejpam-5494	121	15	presents	present	NOUN
ejpam-5494	121	16	revealed	reveal	VERB
ejpam-5494	121	17	examples	example	NOUN
ejpam-5494	121	18	that	that	PRON
ejpam-5494	121	19	support	support	VERB
ejpam-5494	121	20	its	its	PRON
ejpam-5494	121	21	suggested	suggest	VERB
ejpam-5494	121	22	concept	concept	NOUN
ejpam-5494	121	23	.	.	PUNCT
ejpam-5494	122	1	p.	p.	NOUN
ejpam-5494	122	2	pue	pue	PROPN
ejpam-5494	122	3	-	-	PUNCT
ejpam-5494	122	4	on	on	ADP
ejpam-5494	122	5	/	/	SYM
ejpam-5494	122	6	eur	eur	NOUN
ejpam-5494	122	7	.	.	PUNCT
ejpam-5494	123	1	j.	j.	PROPN
ejpam-5494	123	2	pure	pure	PROPN
ejpam-5494	123	3	appl	appl	PROPN
ejpam-5494	123	4	.	.	PROPN
ejpam-5494	123	5	math	math	PROPN
ejpam-5494	123	6	,	,	PUNCT
ejpam-5494	123	7	17	17	NUM
ejpam-5494	123	8	(	(	PUNCT
ejpam-5494	123	9	4	4	NUM
ejpam-5494	123	10	)	)	PUNCT
ejpam-5494	123	11	(	(	PUNCT
ejpam-5494	123	12	2024	2024	NUM
ejpam-5494	123	13	)	)	PUNCT
ejpam-5494	123	14	,	,	PUNCT
ejpam-5494	123	15	3826	3826	NUM
ejpam-5494	123	16	-	-	SYM
ejpam-5494	123	17	3846	3846	NUM
ejpam-5494	123	18	3831	3831	NUM
ejpam-5494	123	19	3.1	3.1	NUM
ejpam-5494	123	20	.	.	PUNCT
ejpam-5494	124	1	implementation	implementation	NOUN
ejpam-5494	124	2	of	of	ADP
ejpam-5494	124	3	the	the	DET
ejpam-5494	124	4	sadik	sadik	PROPN
ejpam-5494	124	5	residual	residual	ADJ
ejpam-5494	124	6	power	power	NOUN
ejpam-5494	124	7	series	series	NOUN
ejpam-5494	124	8	method	method	NOUN
ejpam-5494	124	9	in	in	ADP
ejpam-5494	124	10	a	a	DET
ejpam-5494	124	11	system	system	NOUN
ejpam-5494	124	12	of	of	ADP
ejpam-5494	124	13	time	time	NOUN
ejpam-5494	124	14	-	-	PUNCT
ejpam-5494	124	15	fractional	fractional	ADJ
ejpam-5494	124	16	pdes	pde	NOUN
ejpam-5494	124	17	consider	consider	VERB
ejpam-5494	124	18	the	the	DET
ejpam-5494	124	19	nonlinear	nonlinear	ADJ
ejpam-5494	124	20	system	system	NOUN
ejpam-5494	124	21	of	of	ADP
ejpam-5494	124	22	time	time	NOUN
ejpam-5494	124	23	-	-	PUNCT
ejpam-5494	124	24	fractional	fractional	ADJ
ejpam-5494	124	25	partial	partial	ADJ
ejpam-5494	124	26	differential	differential	NOUN
ejpam-5494	124	27	equation	equation	NOUN
ejpam-5494	124	28	(	(	PUNCT
ejpam-5494	124	29	1	1	X
ejpam-5494	124	30	)	)	PUNCT
ejpam-5494	124	31	dγ	dγ	ADP
ejpam-5494	124	32	t	t	PROPN
ejpam-5494	124	33	ui(x	ui(x	PROPN
ejpam-5494	124	34	,	,	PUNCT
ejpam-5494	124	35	t	t	PROPN
ejpam-5494	124	36	)	)	PUNCT
ejpam-5494	124	37	=	=	SYM
ejpam-5494	124	38	ni(uj(x	ni(uj(x	PROPN
ejpam-5494	124	39	,	,	PUNCT
ejpam-5494	124	40	t),x	t),x	PROPN
ejpam-5494	124	41	,	,	PUNCT
ejpam-5494	124	42	t	t	PROPN
ejpam-5494	124	43	)	)	PUNCT
ejpam-5494	124	44	+	+	SYM
ejpam-5494	124	45	fi(x	fi(x	NUM
ejpam-5494	124	46	,	,	PUNCT
ejpam-5494	124	47	t	t	PROPN
ejpam-5494	124	48	)	)	PUNCT
ejpam-5494	124	49	,	,	PUNCT
ejpam-5494	124	50	i	i	PRON
ejpam-5494	124	51	=	=	NOUN
ejpam-5494	124	52	1	1	NUM
ejpam-5494	124	53	,	,	PUNCT
ejpam-5494	124	54	.	.	PUNCT
ejpam-5494	124	55	.	.	PUNCT
ejpam-5494	125	1	.	.	PUNCT
ejpam-5494	126	1	,	,	PUNCT
ejpam-5494	126	2	n	n	CCONJ
ejpam-5494	126	3	with	with	ADP
ejpam-5494	126	4	initial	initial	ADJ
ejpam-5494	126	5	conditions	condition	NOUN
ejpam-5494	126	6	ui(x	ui(x	ADJ
ejpam-5494	126	7	,	,	PUNCT
ejpam-5494	126	8	0	0	NUM
ejpam-5494	126	9	)	)	PUNCT
ejpam-5494	126	10	=	=	SYM
ejpam-5494	126	11	gi(x	gi(x	PROPN
ejpam-5494	126	12	)	)	PUNCT
ejpam-5494	126	13	.	.	PUNCT
ejpam-5494	127	1	applying	apply	VERB
ejpam-5494	127	2	the	the	DET
ejpam-5494	127	3	sadik	sadik	PROPN
ejpam-5494	127	4	transform	transform	NOUN
ejpam-5494	127	5	and	and	CCONJ
ejpam-5494	127	6	along	along	ADP
ejpam-5494	127	7	with	with	ADP
ejpam-5494	127	8	the	the	DET
ejpam-5494	127	9	initial	initial	ADJ
ejpam-5494	127	10	condition	condition	NOUN
ejpam-5494	127	11	yields	yield	NOUN
ejpam-5494	127	12	vγαui(x	vγαui(x	PROPN
ejpam-5494	127	13	,	,	PUNCT
ejpam-5494	127	14	v	v	ADP
ejpam-5494	127	15	α	α	NOUN
ejpam-5494	127	16	,	,	PUNCT
ejpam-5494	127	17	β)−	β)−	ADJ
ejpam-5494	127	18	v(γ−1)α−βgi(x	v(γ−1)α−βgi(x	NOUN
ejpam-5494	127	19	)	)	PUNCT
ejpam-5494	127	20	=	=	SYM
ejpam-5494	127	21	s	s	X
ejpam-5494	127	22	[	[	PUNCT
ejpam-5494	127	23	ni(uj(x	ni(uj(x	PROPN
ejpam-5494	127	24	,	,	PUNCT
ejpam-5494	127	25	t),x	t),x	PROPN
ejpam-5494	127	26	,	,	PUNCT
ejpam-5494	127	27	t	t	PROPN
ejpam-5494	127	28	)	)	PUNCT
ejpam-5494	127	29	]	]	PUNCT
ejpam-5494	128	1	+	+	CCONJ
ejpam-5494	128	2	fi(x	fi(x	NUM
ejpam-5494	128	3	,	,	PUNCT
ejpam-5494	128	4	v	v	NOUN
ejpam-5494	128	5	α	α	NOUN
ejpam-5494	128	6	,	,	PUNCT
ejpam-5494	128	7	β	β	NOUN
ejpam-5494	128	8	)	)	PUNCT
ejpam-5494	128	9	.	.	PUNCT
ejpam-5494	129	1	rearranging	rearrange	VERB
ejpam-5494	129	2	the	the	DET
ejpam-5494	129	3	equation	equation	NOUN
ejpam-5494	129	4	obtained	obtain	VERB
ejpam-5494	129	5	ui(x	ui(x	PROPN
ejpam-5494	129	6	,	,	PUNCT
ejpam-5494	129	7	v	v	ADP
ejpam-5494	129	8	α	α	NUM
ejpam-5494	129	9	,	,	PUNCT
ejpam-5494	129	10	β	β	NOUN
ejpam-5494	129	11	)	)	PUNCT
ejpam-5494	129	12	=	=	SYM
ejpam-5494	129	13	1	1	NUM
ejpam-5494	129	14	vα+β	vα+β	NUM
ejpam-5494	129	15	gi(x	gi(x	NOUN
ejpam-5494	129	16	)	)	PUNCT
ejpam-5494	130	1	+	+	CCONJ
ejpam-5494	130	2	1	1	NUM
ejpam-5494	130	3	vγα	vγα	PROPN
ejpam-5494	130	4	s	s	X
ejpam-5494	130	5	[	[	PUNCT
ejpam-5494	130	6	ni(uj(x	ni(uj(x	PROPN
ejpam-5494	130	7	,	,	PUNCT
ejpam-5494	130	8	t),x	t),x	PROPN
ejpam-5494	130	9	,	,	PUNCT
ejpam-5494	130	10	t	t	PROPN
ejpam-5494	130	11	)	)	PUNCT
ejpam-5494	130	12	]	]	PUNCT
ejpam-5494	131	1	+	+	CCONJ
ejpam-5494	131	2	1	1	NUM
ejpam-5494	131	3	vγα	vγα	PROPN
ejpam-5494	131	4	fi(x	fi(x	NOUN
ejpam-5494	131	5	,	,	PUNCT
ejpam-5494	131	6	v	v	NOUN
ejpam-5494	131	7	α	α	NOUN
ejpam-5494	131	8	,	,	PUNCT
ejpam-5494	131	9	β	β	NOUN
ejpam-5494	131	10	)	)	PUNCT
ejpam-5494	131	11	.	.	PUNCT
ejpam-5494	132	1	performing	perform	VERB
ejpam-5494	132	2	the	the	DET
ejpam-5494	132	3	inverse	inverse	NOUN
ejpam-5494	132	4	sadik	sadik	PROPN
ejpam-5494	132	5	transform	transform	VERB
ejpam-5494	132	6	results	result	NOUN
ejpam-5494	132	7	in	in	ADP
ejpam-5494	132	8	ui(x	ui(x	PROPN
ejpam-5494	132	9	,	,	PUNCT
ejpam-5494	132	10	t	t	PROPN
ejpam-5494	132	11	)	)	PUNCT
ejpam-5494	132	12	=	=	PUNCT
ejpam-5494	132	13	gi(x	gi(x	X
ejpam-5494	132	14	)	)	PUNCT
ejpam-5494	133	1	+	+	CCONJ
ejpam-5494	133	2	s−1	s−1	PROPN
ejpam-5494	133	3	[	[	PUNCT
ejpam-5494	133	4	1	1	NUM
ejpam-5494	133	5	vγα	vγα	NOUN
ejpam-5494	133	6	s	s	X
ejpam-5494	133	7	[	[	PUNCT
ejpam-5494	133	8	ni(uj(x	ni(uj(x	PROPN
ejpam-5494	133	9	,	,	PUNCT
ejpam-5494	133	10	t),x	t),x	PROPN
ejpam-5494	133	11	,	,	PUNCT
ejpam-5494	133	12	t	t	PROPN
ejpam-5494	133	13	)	)	PUNCT
ejpam-5494	133	14	]	]	PUNCT
ejpam-5494	133	15	]	]	X
ejpam-5494	134	1	+	+	CCONJ
ejpam-5494	134	2	s−1	s−1	PROPN
ejpam-5494	134	3	[	[	PUNCT
ejpam-5494	134	4	1	1	NUM
ejpam-5494	134	5	vγα	vγα	PROPN
ejpam-5494	134	6	fi(x	fi(x	NOUN
ejpam-5494	134	7	,	,	PUNCT
ejpam-5494	134	8	v	v	NOUN
ejpam-5494	134	9	α	α	NOUN
ejpam-5494	134	10	,	,	PUNCT
ejpam-5494	134	11	β	β	NOUN
ejpam-5494	134	12	)	)	PUNCT
ejpam-5494	134	13	]	]	PUNCT
ejpam-5494	134	14	.	.	PUNCT
ejpam-5494	135	1	assume	assume	VERB
ejpam-5494	135	2	the	the	DET
ejpam-5494	135	3	solution	solution	NOUN
ejpam-5494	135	4	to	to	ADP
ejpam-5494	135	5	(	(	PUNCT
ejpam-5494	135	6	1	1	X
ejpam-5494	135	7	)	)	PUNCT
ejpam-5494	135	8	is	be	AUX
ejpam-5494	135	9	provided	provide	VERB
ejpam-5494	135	10	within	within	ADP
ejpam-5494	135	11	the	the	DET
ejpam-5494	135	12	infinite	infinite	ADJ
ejpam-5494	135	13	series	series	NOUN
ejpam-5494	135	14	ui(x	ui(x	PROPN
ejpam-5494	135	15	,	,	PUNCT
ejpam-5494	135	16	t	t	PROPN
ejpam-5494	135	17	)	)	PUNCT
ejpam-5494	135	18	=	=	PUNCT
ejpam-5494	136	1	∞∑	∞∑	PRON
ejpam-5494	136	2	n=0	n=0	NUM
ejpam-5494	136	3	ai	ai	VERB
ejpam-5494	136	4	,	,	PUNCT
ejpam-5494	136	5	n(x	n(x	ADJ
ejpam-5494	136	6	)	)	PUNCT
ejpam-5494	136	7	tnγ	tnγ	NOUN
ejpam-5494	136	8	γ(nγ	γ(nγ	NOUN
ejpam-5494	136	9	+	+	CCONJ
ejpam-5494	136	10	1	1	NUM
ejpam-5494	136	11	)	)	PUNCT
ejpam-5494	136	12	.	.	PUNCT
ejpam-5494	137	1	(	(	PUNCT
ejpam-5494	137	2	6	6	NUM
ejpam-5494	137	3	)	)	PUNCT
ejpam-5494	137	4	according	accord	VERB
ejpam-5494	137	5	to	to	ADP
ejpam-5494	137	6	the	the	DET
ejpam-5494	137	7	residual	residual	ADJ
ejpam-5494	137	8	power	power	NOUN
ejpam-5494	137	9	series	series	NOUN
ejpam-5494	137	10	strategy	strategy	NOUN
ejpam-5494	137	11	,	,	PUNCT
ejpam-5494	137	12	we	we	PRON
ejpam-5494	137	13	define	define	VERB
ejpam-5494	137	14	the	the	DET
ejpam-5494	137	15	residual	residual	ADJ
ejpam-5494	137	16	function	function	NOUN
ejpam-5494	137	17	as	as	SCONJ
ejpam-5494	137	18	follows	follow	VERB
ejpam-5494	137	19	resi(x	resi(x	PROPN
ejpam-5494	137	20	,	,	PUNCT
ejpam-5494	137	21	t	t	PROPN
ejpam-5494	137	22	)	)	PUNCT
ejpam-5494	137	23	=	=	SYM
ejpam-5494	138	1	ui(x	ui(x	ADJ
ejpam-5494	138	2	,	,	PUNCT
ejpam-5494	138	3	t)−	t)−	PROPN
ejpam-5494	138	4	gi(x)−	gi(x)−	PROPN
ejpam-5494	138	5	s−1	s−1	PROPN
ejpam-5494	138	6	[	[	PUNCT
ejpam-5494	138	7	1	1	NUM
ejpam-5494	138	8	vγα	vγα	PROPN
ejpam-5494	138	9	s	s	X
ejpam-5494	138	10	[	[	PUNCT
ejpam-5494	138	11	ni(uj(x	ni(uj(x	PROPN
ejpam-5494	138	12	,	,	PUNCT
ejpam-5494	138	13	t),x	t),x	PROPN
ejpam-5494	138	14	,	,	PUNCT
ejpam-5494	138	15	t	t	PROPN
ejpam-5494	138	16	)	)	PUNCT
ejpam-5494	138	17	]	]	PUNCT
ejpam-5494	138	18	]	]	PUNCT
ejpam-5494	139	1	−	−	PROPN
ejpam-5494	139	2	s−1	s−1	PROPN
ejpam-5494	139	3	[	[	PUNCT
ejpam-5494	139	4	1	1	NUM
ejpam-5494	139	5	vγα	vγα	PROPN
ejpam-5494	139	6	fi(x	fi(x	NOUN
ejpam-5494	139	7	,	,	PUNCT
ejpam-5494	139	8	v	v	NOUN
ejpam-5494	139	9	α	α	NOUN
ejpam-5494	139	10	,	,	PUNCT
ejpam-5494	139	11	β	β	NOUN
ejpam-5494	139	12	)	)	PUNCT
ejpam-5494	139	13	]	]	PUNCT
ejpam-5494	139	14	,	,	PUNCT
ejpam-5494	139	15	and	and	CCONJ
ejpam-5494	139	16	the	the	DET
ejpam-5494	139	17	kth	kth	PROPN
ejpam-5494	139	18	truncated	truncate	VERB
ejpam-5494	139	19	series	series	NOUN
ejpam-5494	139	20	of	of	ADP
ejpam-5494	139	21	(	(	PUNCT
ejpam-5494	139	22	6	6	NUM
ejpam-5494	139	23	)	)	PUNCT
ejpam-5494	139	24	is	be	AUX
ejpam-5494	139	25	stated	state	VERB
ejpam-5494	139	26	as	as	ADP
ejpam-5494	139	27	uk(x	uk(x	NOUN
ejpam-5494	139	28	,	,	PUNCT
ejpam-5494	139	29	t	t	PROPN
ejpam-5494	139	30	)	)	PUNCT
ejpam-5494	139	31	=	=	PUNCT
ejpam-5494	140	1	k∑	k∑	PROPN
ejpam-5494	140	2	n=0	n=0	PROPN
ejpam-5494	140	3	ai	ai	VERB
ejpam-5494	140	4	,	,	PUNCT
ejpam-5494	140	5	n(x	n(x	ADJ
ejpam-5494	140	6	)	)	PUNCT
ejpam-5494	140	7	tnγ	tnγ	NOUN
ejpam-5494	140	8	γ(nγ	γ(nγ	NOUN
ejpam-5494	140	9	+	+	CCONJ
ejpam-5494	140	10	1	1	NUM
ejpam-5494	140	11	)	)	PUNCT
ejpam-5494	140	12	.	.	PUNCT
ejpam-5494	141	1	since	since	SCONJ
ejpam-5494	141	2	the	the	DET
ejpam-5494	141	3	solution	solution	NOUN
ejpam-5494	141	4	satisfies	satisfy	VERB
ejpam-5494	141	5	the	the	DET
ejpam-5494	141	6	initial	initial	ADJ
ejpam-5494	141	7	condition	condition	NOUN
ejpam-5494	141	8	,	,	PUNCT
ejpam-5494	141	9	ai,0(x	ai,0(x	NOUN
ejpam-5494	141	10	)	)	PUNCT
ejpam-5494	141	11	=	=	PUNCT
ejpam-5494	141	12	gi(x	gi(x	PROPN
ejpam-5494	141	13	)	)	PUNCT
ejpam-5494	141	14	.	.	PUNCT
ejpam-5494	142	1	hence	hence	ADV
ejpam-5494	142	2	,	,	PUNCT
ejpam-5494	142	3	the	the	DET
ejpam-5494	142	4	korder	korder	NOUN
ejpam-5494	142	5	approximated	approximate	VERB
ejpam-5494	142	6	solution	solution	NOUN
ejpam-5494	142	7	turns	turn	VERB
ejpam-5494	142	8	into	into	ADP
ejpam-5494	142	9	ui	ui	PROPN
ejpam-5494	142	10	,	,	PUNCT
ejpam-5494	142	11	k(x	k(x	PROPN
ejpam-5494	142	12	,	,	PUNCT
ejpam-5494	142	13	t	t	PROPN
ejpam-5494	142	14	)	)	PUNCT
ejpam-5494	142	15	=	=	PUNCT
ejpam-5494	142	16	gi(x	gi(x	X
ejpam-5494	142	17	)	)	PUNCT
ejpam-5494	143	1	+	+	CCONJ
ejpam-5494	143	2	k∑	k∑	VERB
ejpam-5494	143	3	n=1	n=1	PROPN
ejpam-5494	143	4	ai	ai	VERB
ejpam-5494	143	5	,	,	PUNCT
ejpam-5494	143	6	n(x	n(x	X
ejpam-5494	143	7	)	)	PUNCT
ejpam-5494	143	8	tnγ	tnγ	NOUN
ejpam-5494	143	9	γ(nγ	γ(nγ	NOUN
ejpam-5494	143	10	+	+	CCONJ
ejpam-5494	143	11	1	1	NUM
ejpam-5494	143	12	)	)	PUNCT
ejpam-5494	143	13	.	.	PUNCT
ejpam-5494	144	1	(	(	PUNCT
ejpam-5494	144	2	7	7	X
ejpam-5494	144	3	)	)	PUNCT
ejpam-5494	144	4	furthermore	furthermore	ADV
ejpam-5494	144	5	,	,	PUNCT
ejpam-5494	144	6	the	the	DET
ejpam-5494	144	7	kresidual	kresidual	ADJ
ejpam-5494	144	8	function	function	NOUN
ejpam-5494	144	9	is	be	AUX
ejpam-5494	144	10	expressed	express	VERB
ejpam-5494	144	11	as	as	ADP
ejpam-5494	144	12	resi	resi	PROPN
ejpam-5494	144	13	,	,	PUNCT
ejpam-5494	144	14	k(x	k(x	PROPN
ejpam-5494	144	15	,	,	PUNCT
ejpam-5494	144	16	t	t	PROPN
ejpam-5494	144	17	)	)	PUNCT
ejpam-5494	144	18	=	=	SYM
ejpam-5494	144	19	ui	ui	PROPN
ejpam-5494	144	20	,	,	PUNCT
ejpam-5494	144	21	k(x	k(x	PROPN
ejpam-5494	144	22	,	,	PUNCT
ejpam-5494	144	23	t)−	t)−	PROPN
ejpam-5494	144	24	gi(x)−	gi(x)−	PROPN
ejpam-5494	144	25	s−1	s−1	PROPN
ejpam-5494	144	26	[	[	PUNCT
ejpam-5494	144	27	1	1	NUM
ejpam-5494	144	28	vγα	vγα	PROPN
ejpam-5494	144	29	s	s	X
ejpam-5494	144	30	[	[	PUNCT
ejpam-5494	144	31	ni(uj	ni(uj	PROPN
ejpam-5494	144	32	,	,	PUNCT
ejpam-5494	144	33	k(x	k(x	PROPN
ejpam-5494	144	34	,	,	PUNCT
ejpam-5494	144	35	t),x	t),x	PROPN
ejpam-5494	144	36	,	,	PUNCT
ejpam-5494	144	37	t	t	PROPN
ejpam-5494	144	38	)	)	PUNCT
ejpam-5494	144	39	]	]	PUNCT
ejpam-5494	144	40	]	]	PUNCT
ejpam-5494	145	1	−	−	PROPN
ejpam-5494	145	2	s−1	s−1	PROPN
ejpam-5494	145	3	[	[	PUNCT
ejpam-5494	145	4	1	1	NUM
ejpam-5494	145	5	vγα	vγα	PROPN
ejpam-5494	145	6	fi(x	fi(x	NOUN
ejpam-5494	145	7	,	,	PUNCT
ejpam-5494	145	8	v	v	NOUN
ejpam-5494	145	9	α	α	NOUN
ejpam-5494	145	10	,	,	PUNCT
ejpam-5494	145	11	β	β	NOUN
ejpam-5494	145	12	)	)	PUNCT
ejpam-5494	145	13	]	]	PUNCT
ejpam-5494	145	14	.	.	PUNCT
ejpam-5494	146	1	p.	p.	NOUN
ejpam-5494	146	2	pue	pue	NOUN
ejpam-5494	146	3	-	-	PUNCT
ejpam-5494	146	4	on	on	ADP
ejpam-5494	146	5	/	/	SYM
ejpam-5494	146	6	eur	eur	NOUN
ejpam-5494	146	7	.	.	PUNCT
ejpam-5494	147	1	j.	j.	PROPN
ejpam-5494	147	2	pure	pure	PROPN
ejpam-5494	147	3	appl	appl	PROPN
ejpam-5494	147	4	.	.	PROPN
ejpam-5494	147	5	math	math	PROPN
ejpam-5494	147	6	,	,	PUNCT
ejpam-5494	147	7	17	17	NUM
ejpam-5494	147	8	(	(	PUNCT
ejpam-5494	147	9	4	4	NUM
ejpam-5494	147	10	)	)	PUNCT
ejpam-5494	147	11	(	(	PUNCT
ejpam-5494	147	12	2024	2024	NUM
ejpam-5494	147	13	)	)	PUNCT
ejpam-5494	147	14	,	,	PUNCT
ejpam-5494	147	15	3826	3826	NUM
ejpam-5494	147	16	-	-	SYM
ejpam-5494	147	17	3846	3846	NUM
ejpam-5494	147	18	3832	3832	NUM
ejpam-5494	147	19	for	for	ADP
ejpam-5494	147	20	the	the	DET
ejpam-5494	147	21	calculation	calculation	NOUN
ejpam-5494	147	22	of	of	ADP
ejpam-5494	147	23	the	the	DET
ejpam-5494	147	24	coefficients	coefficient	NOUN
ejpam-5494	147	25	ai	ai	VERB
ejpam-5494	147	26	,	,	PUNCT
ejpam-5494	147	27	n(x	n(x	PROPN
ejpam-5494	147	28	)	)	PUNCT
ejpam-5494	147	29	,	,	PUNCT
ejpam-5494	147	30	n	n	NOUN
ejpam-5494	147	31	=	=	SYM
ejpam-5494	147	32	1	1	NUM
ejpam-5494	147	33	,	,	PUNCT
ejpam-5494	147	34	2	2	NUM
ejpam-5494	147	35	,	,	PUNCT
ejpam-5494	147	36	3	3	NUM
ejpam-5494	147	37	,	,	PUNCT
ejpam-5494	147	38	.	.	PUNCT
ejpam-5494	147	39	.	.	PUNCT
ejpam-5494	148	1	.	.	PUNCT
ejpam-5494	149	1	in	in	ADP
ejpam-5494	149	2	equation	equation	NOUN
ejpam-5494	149	3	(	(	PUNCT
ejpam-5494	149	4	7	7	NUM
ejpam-5494	149	5	)	)	PUNCT
ejpam-5494	149	6	,	,	PUNCT
ejpam-5494	149	7	construct	construct	VERB
ejpam-5494	149	8	the	the	DET
ejpam-5494	149	9	relation	relation	NOUN
ejpam-5494	149	10	for	for	ADP
ejpam-5494	149	11	recurrence	recurrence	NUM
ejpam-5494	149	12	ui,0(x	ui,0(x	PROPN
ejpam-5494	149	13	,	,	PUNCT
ejpam-5494	149	14	t	t	PROPN
ejpam-5494	149	15	)	)	PUNCT
ejpam-5494	149	16	=	=	SYM
ejpam-5494	149	17	gi(x	gi(x	X
ejpam-5494	149	18	)	)	PUNCT
ejpam-5494	149	19	resi	resi	PROPN
ejpam-5494	149	20	,	,	PUNCT
ejpam-5494	149	21	k(x	k(x	PROPN
ejpam-5494	149	22	,	,	PUNCT
ejpam-5494	149	23	t	t	PROPN
ejpam-5494	149	24	)	)	PUNCT
ejpam-5494	149	25	=	=	SYM
ejpam-5494	149	26	ui	ui	PROPN
ejpam-5494	149	27	,	,	PUNCT
ejpam-5494	149	28	k(x	k(x	PROPN
ejpam-5494	149	29	,	,	PUNCT
ejpam-5494	149	30	t)−	t)−	PROPN
ejpam-5494	149	31	gi(x)−	gi(x)−	PROPN
ejpam-5494	149	32	s−1	s−1	PROPN
ejpam-5494	149	33	[	[	PUNCT
ejpam-5494	149	34	1	1	NUM
ejpam-5494	149	35	vγα	vγα	PROPN
ejpam-5494	149	36	s	s	X
ejpam-5494	149	37	[	[	PUNCT
ejpam-5494	149	38	ni(uj	ni(uj	PROPN
ejpam-5494	149	39	,	,	PUNCT
ejpam-5494	149	40	k(x	k(x	PROPN
ejpam-5494	149	41	,	,	PUNCT
ejpam-5494	149	42	t),x	t),x	PROPN
ejpam-5494	149	43	,	,	PUNCT
ejpam-5494	149	44	t	t	PROPN
ejpam-5494	149	45	)	)	PUNCT
ejpam-5494	149	46	]	]	PUNCT
ejpam-5494	149	47	]	]	PUNCT
ejpam-5494	150	1	−	−	PROPN
ejpam-5494	150	2	s−1	s−1	PROPN
ejpam-5494	150	3	[	[	PUNCT
ejpam-5494	150	4	1	1	NUM
ejpam-5494	150	5	vγα	vγα	PROPN
ejpam-5494	150	6	fi(x	fi(x	NOUN
ejpam-5494	150	7	,	,	PUNCT
ejpam-5494	150	8	v	v	NOUN
ejpam-5494	150	9	α	α	NOUN
ejpam-5494	150	10	,	,	PUNCT
ejpam-5494	150	11	β	β	NOUN
ejpam-5494	150	12	)	)	PUNCT
ejpam-5494	150	13	]	]	PUNCT
ejpam-5494	150	14	(	(	PUNCT
ejpam-5494	150	15	8)	8)	NUM
ejpam-5494	150	16	and	and	CCONJ
ejpam-5494	150	17	and	and	CCONJ
ejpam-5494	150	18	afterward	afterward	ADV
ejpam-5494	150	19	follow	follow	VERB
ejpam-5494	150	20	the	the	DET
ejpam-5494	150	21	condition	condition	NOUN
ejpam-5494	150	22	[	[	X
ejpam-5494	150	23	29	29	NUM
ejpam-5494	150	24	]	]	X
ejpam-5494	150	25	t−kα	t−kα	NOUN
ejpam-5494	150	26	·	·	PUNCT
ejpam-5494	150	27	resi	resi	PROPN
ejpam-5494	150	28	,	,	PUNCT
ejpam-5494	150	29	k(x	k(x	PROPN
ejpam-5494	150	30	,	,	PUNCT
ejpam-5494	150	31	t	t	PROPN
ejpam-5494	150	32	)	)	PUNCT
ejpam-5494	150	33	∣∣∣	∣∣∣	NOUN
ejpam-5494	150	34	t=0	t=0	PROPN
ejpam-5494	150	35	=	=	SYM
ejpam-5494	150	36	0	0	X
ejpam-5494	150	37	.	.	PUNCT
ejpam-5494	151	1	(	(	PUNCT
ejpam-5494	151	2	9	9	X
ejpam-5494	151	3	)	)	PUNCT
ejpam-5494	151	4	convergence	convergence	NOUN
ejpam-5494	151	5	criteria	criterion	NOUN
ejpam-5494	151	6	for	for	ADP
ejpam-5494	151	7	sadik	sadik	ADJ
ejpam-5494	151	8	residual	residual	ADJ
ejpam-5494	151	9	power	power	NOUN
ejpam-5494	151	10	series	series	PROPN
ejpam-5494	151	11	method	method	NOUN
ejpam-5494	151	12	theorem	theorem	VERB
ejpam-5494	151	13	5	5	NUM
ejpam-5494	151	14	.	.	PUNCT
ejpam-5494	152	1	[	[	X
ejpam-5494	152	2	8	8	NUM
ejpam-5494	152	3	]	]	PUNCT
ejpam-5494	152	4	let	let	VERB
ejpam-5494	152	5	the	the	DET
ejpam-5494	152	6	banach	banach	NOUN
ejpam-5494	152	7	space	space	NOUN
ejpam-5494	152	8	b	b	PROPN
ejpam-5494	152	9	≡	≡	PROPN
ejpam-5494	152	10	c(x	c(x	PROPN
ejpam-5494	152	11	×	×	NOUN
ejpam-5494	152	12	[	[	X
ejpam-5494	152	13	0	0	NUM
ejpam-5494	152	14	,	,	PUNCT
ejpam-5494	152	15	t	t	X
ejpam-5494	152	16	]	]	PUNCT
ejpam-5494	152	17	)	)	PUNCT
ejpam-5494	152	18	is	be	AUX
ejpam-5494	152	19	defined	define	VERB
ejpam-5494	152	20	on	on	ADP
ejpam-5494	152	21	x	x	X
ejpam-5494	152	22	×	×	NOUN
ejpam-5494	152	23	[	[	X
ejpam-5494	152	24	0	0	NUM
ejpam-5494	152	25	,	,	PUNCT
ejpam-5494	152	26	t	t	X
ejpam-5494	152	27	]	]	PUNCT
ejpam-5494	152	28	,	,	PUNCT
ejpam-5494	152	29	where	where	SCONJ
ejpam-5494	152	30	x	x	X
ejpam-5494	152	31	=	=	PUNCT
ejpam-5494	153	1	[	[	X
ejpam-5494	153	2	a1	a1	NOUN
ejpam-5494	153	3	,	,	PUNCT
ejpam-5494	153	4	b1]×	b1]×	PROPN
ejpam-5494	153	5	[	[	X
ejpam-5494	153	6	a2	a2	PROPN
ejpam-5494	153	7	,	,	PUNCT
ejpam-5494	153	8	b2]×	b2]×	NOUN
ejpam-5494	153	9	.	.	PUNCT
ejpam-5494	153	10	.	.	PUNCT
ejpam-5494	154	1	.×	.×	NOUN
ejpam-5494	155	1	[	[	X
ejpam-5494	155	2	an	an	X
ejpam-5494	155	3	,	,	PUNCT
ejpam-5494	155	4	bn	bn	NOUN
ejpam-5494	155	5	]	]	PUNCT
ejpam-5494	155	6	,	,	PUNCT
ejpam-5494	155	7	then	then	ADV
ejpam-5494	155	8	eq	eq	ADP
ejpam-5494	155	9	.	.	PUNCT
ejpam-5494	156	1	(	(	PUNCT
ejpam-5494	156	2	6	6	NUM
ejpam-5494	156	3	)	)	PUNCT
ejpam-5494	156	4	as	as	ADP
ejpam-5494	156	5	u(x	u(x	NOUN
ejpam-5494	156	6	,	,	PUNCT
ejpam-5494	156	7	t	t	NOUN
ejpam-5494	156	8	)	)	PUNCT
ejpam-5494	156	9	=	=	PUNCT
ejpam-5494	157	1	∑k	∑k	PROPN
ejpam-5494	157	2	n=0	n=0	NUM
ejpam-5494	157	3	uk(x	uk(x	ADP
ejpam-5494	157	4	,	,	PUNCT
ejpam-5494	157	5	t	t	PROPN
ejpam-5494	157	6	)	)	PUNCT
ejpam-5494	157	7	is	be	AUX
ejpam-5494	157	8	convergent	convergent	ADJ
ejpam-5494	157	9	series	series	NOUN
ejpam-5494	157	10	,	,	PUNCT
ejpam-5494	157	11	if	if	SCONJ
ejpam-5494	157	12	u0	u0	PROPN
ejpam-5494	157	13	∈	∈	PROPN
ejpam-5494	157	14	b	b	PROPN
ejpam-5494	157	15	is	be	AUX
ejpam-5494	157	16	bounded	bound	VERB
ejpam-5494	157	17	and	and	CCONJ
ejpam-5494	157	18	∀uk	∀uk	PROPN
ejpam-5494	157	19	∈	∈	PROPN
ejpam-5494	157	20	b	b	PROPN
ejpam-5494	157	21	,	,	PUNCT
ejpam-5494	157	22	∥uk+1∥	∥uk+1∥	NUM
ejpam-5494	157	23	⩽	⩽	NOUN
ejpam-5494	157	24	λ∥uk∥	λ∥uk∥	NOUN
ejpam-5494	157	25	,	,	PUNCT
ejpam-5494	157	26	where	where	SCONJ
ejpam-5494	157	27	0	0	X
ejpam-5494	157	28	<	<	X
ejpam-5494	157	29	λ	λ	X
ejpam-5494	157	30	<	<	X
ejpam-5494	157	31	1	1	NUM
ejpam-5494	157	32	and	and	CCONJ
ejpam-5494	157	33	∥u∥	∥u∥	NOUN
ejpam-5494	157	34	=	=	SYM
ejpam-5494	157	35	supx∈x	supx∈x	PROPN
ejpam-5494	157	36	,	,	PUNCT
ejpam-5494	157	37	t∈[0,t	t∈[0,t	X
ejpam-5494	157	38	]	]	PUNCT
ejpam-5494	158	1	|u(x	|u(x	NOUN
ejpam-5494	158	2	,	,	PUNCT
ejpam-5494	158	3	t)|	t)|	NOUN
ejpam-5494	158	4	.	.	PUNCT
ejpam-5494	159	1	theorem	theorem	VERB
ejpam-5494	159	2	6	6	NUM
ejpam-5494	159	3	.	.	PUNCT
ejpam-5494	160	1	[	[	X
ejpam-5494	160	2	8	8	NUM
ejpam-5494	160	3	]	]	PUNCT
ejpam-5494	160	4	the	the	DET
ejpam-5494	160	5	maximum	maximum	ADJ
ejpam-5494	160	6	absolute	absolute	ADJ
ejpam-5494	160	7	error	error	NOUN
ejpam-5494	160	8	for	for	ADP
ejpam-5494	160	9	(	(	PUNCT
ejpam-5494	160	10	6	6	NUM
ejpam-5494	160	11	)	)	PUNCT
ejpam-5494	160	12	is	be	AUX
ejpam-5494	160	13	defined	define	VERB
ejpam-5494	160	14	by	by	ADP
ejpam-5494	160	15	∥u(x	∥u(x	NOUN
ejpam-5494	160	16	,	,	PUNCT
ejpam-5494	160	17	t)−	t)−	PROPN
ejpam-5494	160	18	k∑	k∑	PROPN
ejpam-5494	160	19	n=0	n=0	PROPN
ejpam-5494	160	20	un(x	un(x	SYM
ejpam-5494	160	21	,	,	PUNCT
ejpam-5494	160	22	t)∥	t)∥	NUM
ejpam-5494	160	23	⩽	⩽	NOUN
ejpam-5494	160	24	λk+1	λk+1	NOUN
ejpam-5494	160	25	1−	1−	NUM
ejpam-5494	160	26	λ	λ	NOUN
ejpam-5494	160	27	∥u0(x	∥u0(x	NOUN
ejpam-5494	160	28	,	,	PUNCT
ejpam-5494	160	29	t)∥.	t)∥.	PRON
ejpam-5494	160	30	remark	remark	NOUN
ejpam-5494	160	31	3	3	NUM
ejpam-5494	160	32	.	.	PUNCT
ejpam-5494	161	1	the	the	DET
ejpam-5494	161	2	procedure	procedure	NOUN
ejpam-5494	161	3	for	for	ADP
ejpam-5494	161	4	proving	prove	VERB
ejpam-5494	161	5	the	the	DET
ejpam-5494	161	6	aforementioned	aforementioned	ADJ
ejpam-5494	161	7	theorems	theorem	NOUN
ejpam-5494	161	8	is	be	AUX
ejpam-5494	161	9	the	the	DET
ejpam-5494	161	10	same	same	ADJ
ejpam-5494	161	11	as	as	ADP
ejpam-5494	161	12	that	that	PRON
ejpam-5494	161	13	used	use	VERB
ejpam-5494	161	14	in	in	ADP
ejpam-5494	161	15	the	the	DET
ejpam-5494	161	16	reference	reference	NOUN
ejpam-5494	161	17	,	,	PUNCT
ejpam-5494	161	18	which	which	PRON
ejpam-5494	161	19	will	will	AUX
ejpam-5494	161	20	not	not	PART
ejpam-5494	161	21	be	be	AUX
ejpam-5494	161	22	examined	examine	VERB
ejpam-5494	161	23	further	far	ADV
ejpam-5494	161	24	here	here	ADV
ejpam-5494	161	25	.	.	PUNCT
ejpam-5494	162	1	3.2	3.2	NUM
ejpam-5494	162	2	.	.	PUNCT
ejpam-5494	163	1	illustrative	illustrative	ADJ
ejpam-5494	163	2	examples	example	NOUN
ejpam-5494	163	3	example	example	NOUN
ejpam-5494	163	4	1	1	NUM
ejpam-5494	163	5	.	.	PUNCT
ejpam-5494	164	1	[	[	X
ejpam-5494	164	2	4	4	X
ejpam-5494	164	3	]	]	PUNCT
ejpam-5494	164	4	consider	consider	VERB
ejpam-5494	164	5	the	the	DET
ejpam-5494	164	6	nonlinear	nonlinear	ADJ
ejpam-5494	164	7	system	system	NOUN
ejpam-5494	164	8	of	of	ADP
ejpam-5494	164	9	fractional	fractional	ADJ
ejpam-5494	164	10	partial	partial	ADJ
ejpam-5494	164	11	differential	differential	NOUN
ejpam-5494	164	12	equation	equation	NOUN
ejpam-5494	164	13	dγ	dγ	PROPN
ejpam-5494	164	14	t	t	PROPN
ejpam-5494	164	15	u(x	u(x	PROPN
ejpam-5494	164	16	,	,	PUNCT
ejpam-5494	164	17	t	t	PROPN
ejpam-5494	164	18	)	)	PUNCT
ejpam-5494	164	19	+	+	NUM
ejpam-5494	164	20	w2(x	w2(x	PROPN
ejpam-5494	164	21	,	,	PUNCT
ejpam-5494	164	22	t)u2x(x	t)u2x(x	NOUN
ejpam-5494	164	23	,	,	PUNCT
ejpam-5494	164	24	t	t	PROPN
ejpam-5494	164	25	)	)	PUNCT
ejpam-5494	165	1	+	+	CCONJ
ejpam-5494	165	2	u(x	u(x	PROPN
ejpam-5494	165	3	,	,	PUNCT
ejpam-5494	165	4	t	t	NOUN
ejpam-5494	165	5	)	)	PUNCT
ejpam-5494	165	6	=	=	SYM
ejpam-5494	165	7	1	1	NUM
ejpam-5494	165	8	,	,	PUNCT
ejpam-5494	165	9	dγ	dγ	ADP
ejpam-5494	165	10	t	t	PROPN
ejpam-5494	165	11	w(x	w(x	PROPN
ejpam-5494	165	12	,	,	PUNCT
ejpam-5494	165	13	t	t	PROPN
ejpam-5494	165	14	)	)	PUNCT
ejpam-5494	166	1	+	+	CCONJ
ejpam-5494	166	2	u2(x	u2(x	SYM
ejpam-5494	166	3	,	,	PUNCT
ejpam-5494	166	4	t)w2	t)w2	PROPN
ejpam-5494	166	5	x(x	x(x	PROPN
ejpam-5494	166	6	,	,	PUNCT
ejpam-5494	166	7	t)−	t)−	PROPN
ejpam-5494	166	8	w(x	w(x	PROPN
ejpam-5494	166	9	,	,	PUNCT
ejpam-5494	166	10	t	t	PROPN
ejpam-5494	166	11	)	)	PUNCT
ejpam-5494	166	12	=	=	SYM
ejpam-5494	166	13	1	1	NUM
ejpam-5494	166	14	,	,	PUNCT
ejpam-5494	166	15	with	with	ADP
ejpam-5494	166	16	initial	initial	ADJ
ejpam-5494	166	17	conditions	condition	NOUN
ejpam-5494	166	18	u(x	u(x	NOUN
ejpam-5494	166	19	,	,	PUNCT
ejpam-5494	166	20	0	0	NUM
ejpam-5494	166	21	)	)	PUNCT
ejpam-5494	166	22	=	=	SYM
ejpam-5494	166	23	ex	ex	X
ejpam-5494	166	24	,	,	PUNCT
ejpam-5494	166	25	w(x	w(x	PROPN
ejpam-5494	166	26	,	,	PUNCT
ejpam-5494	166	27	0	0	NUM
ejpam-5494	166	28	)	)	PUNCT
ejpam-5494	166	29	=	=	SYM
ejpam-5494	166	30	e−x	e−x	NOUN
ejpam-5494	166	31	.	.	PUNCT
ejpam-5494	167	1	the	the	DET
ejpam-5494	167	2	exact	exact	ADJ
ejpam-5494	167	3	solution	solution	NOUN
ejpam-5494	167	4	to	to	ADP
ejpam-5494	167	5	the	the	DET
ejpam-5494	167	6	problem	problem	NOUN
ejpam-5494	167	7	when	when	SCONJ
ejpam-5494	167	8	γ	γ	X
ejpam-5494	167	9	=	=	SYM
ejpam-5494	167	10	1	1	NUM
ejpam-5494	167	11	is	be	AUX
ejpam-5494	167	12	u(x	u(x	NOUN
ejpam-5494	167	13	,	,	PUNCT
ejpam-5494	167	14	t	t	NOUN
ejpam-5494	167	15	)	)	PUNCT
ejpam-5494	168	1	=	=	SYM
ejpam-5494	168	2	ex−t	ex−t	NOUN
ejpam-5494	168	3	,	,	PUNCT
ejpam-5494	168	4	w(x	w(x	PROPN
ejpam-5494	168	5	,	,	PUNCT
ejpam-5494	168	6	t	t	PROPN
ejpam-5494	168	7	)	)	PUNCT
ejpam-5494	168	8	=	=	PUNCT
ejpam-5494	168	9	e−x+t	e−x+t	NOUN
ejpam-5494	168	10	.	.	PUNCT
ejpam-5494	169	1	here	here	ADV
ejpam-5494	169	2	n1(u	n1(u	NOUN
ejpam-5494	169	3	,	,	PUNCT
ejpam-5494	169	4	w	w	NOUN
ejpam-5494	169	5	)	)	PUNCT
ejpam-5494	169	6	=	=	SYM
ejpam-5494	170	1	−w2u2x	−w2u2x	NOUN
ejpam-5494	170	2	−	−	PROPN
ejpam-5494	170	3	u	u	PROPN
ejpam-5494	170	4	,	,	PUNCT
ejpam-5494	170	5	n2(u	n2(u	PROPN
ejpam-5494	170	6	,	,	PUNCT
ejpam-5494	170	7	w	w	NOUN
ejpam-5494	170	8	)	)	PUNCT
ejpam-5494	170	9	=	=	PUNCT
ejpam-5494	171	1	−u2w2	−u2w2	NOUN
ejpam-5494	171	2	x	x	PUNCT
ejpam-5494	172	1	+	+	NUM
ejpam-5494	172	2	w	w	PROPN
ejpam-5494	172	3	,	,	PUNCT
ejpam-5494	172	4	f1(x	f1(x	PROPN
ejpam-5494	172	5	,	,	PUNCT
ejpam-5494	172	6	t	t	PROPN
ejpam-5494	172	7	)	)	PUNCT
ejpam-5494	172	8	=	=	SYM
ejpam-5494	172	9	f2(x	f2(x	PROPN
ejpam-5494	172	10	,	,	PUNCT
ejpam-5494	172	11	t	t	PROPN
ejpam-5494	172	12	)	)	PUNCT
ejpam-5494	172	13	=	=	SYM
ejpam-5494	172	14	1	1	NUM
ejpam-5494	172	15	,	,	PUNCT
ejpam-5494	172	16	g1(x	g1(x	NOUN
ejpam-5494	172	17	)	)	PUNCT
ejpam-5494	172	18	=	=	SYM
ejpam-5494	172	19	ex	ex	X
ejpam-5494	172	20	,	,	PUNCT
ejpam-5494	172	21	g2(x	g2(x	X
ejpam-5494	172	22	)	)	PUNCT
ejpam-5494	172	23	=	=	SYM
ejpam-5494	172	24	e−x	e−x	NOUN
ejpam-5494	172	25	.	.	PUNCT
ejpam-5494	173	1	the	the	DET
ejpam-5494	173	2	kth−	kth−	PROPN
ejpam-5494	173	3	truncated	truncated	ADJ
ejpam-5494	173	4	term	term	NOUN
ejpam-5494	173	5	series	series	NOUN
ejpam-5494	173	6	solution	solution	NOUN
ejpam-5494	173	7	for	for	ADP
ejpam-5494	173	8	this	this	DET
ejpam-5494	173	9	problem	problem	NOUN
ejpam-5494	173	10	is	be	AUX
ejpam-5494	173	11	uk(x	uk(x	ADV
ejpam-5494	173	12	,	,	PUNCT
ejpam-5494	173	13	t	t	PROPN
ejpam-5494	173	14	)	)	PUNCT
ejpam-5494	173	15	=	=	PUNCT
ejpam-5494	173	16	k∑	k∑	PROPN
ejpam-5494	173	17	n=0	n=0	NUM
ejpam-5494	173	18	an(x	an(x	NOUN
ejpam-5494	173	19	)	)	PUNCT
ejpam-5494	173	20	tnγ	tnγ	NOUN
ejpam-5494	173	21	γ(nγ	γ(nγ	NOUN
ejpam-5494	173	22	+	+	CCONJ
ejpam-5494	173	23	1	1	NUM
ejpam-5494	173	24	)	)	PUNCT
ejpam-5494	173	25	,	,	PUNCT
ejpam-5494	174	1	p.	p.	NOUN
ejpam-5494	174	2	pue	pue	PROPN
ejpam-5494	174	3	-	-	PUNCT
ejpam-5494	174	4	on	on	ADP
ejpam-5494	174	5	/	/	SYM
ejpam-5494	174	6	eur	eur	NOUN
ejpam-5494	174	7	.	.	PUNCT
ejpam-5494	175	1	j.	j.	PROPN
ejpam-5494	175	2	pure	pure	PROPN
ejpam-5494	175	3	appl	appl	PROPN
ejpam-5494	175	4	.	.	PROPN
ejpam-5494	175	5	math	math	PROPN
ejpam-5494	175	6	,	,	PUNCT
ejpam-5494	175	7	17	17	NUM
ejpam-5494	175	8	(	(	PUNCT
ejpam-5494	175	9	4	4	NUM
ejpam-5494	175	10	)	)	PUNCT
ejpam-5494	175	11	(	(	PUNCT
ejpam-5494	175	12	2024	2024	NUM
ejpam-5494	175	13	)	)	PUNCT
ejpam-5494	175	14	,	,	PUNCT
ejpam-5494	175	15	3826	3826	NUM
ejpam-5494	175	16	-	-	SYM
ejpam-5494	175	17	3846	3846	NUM
ejpam-5494	175	18	3833	3833	NUM
ejpam-5494	175	19	wk(x	wk(x	PROPN
ejpam-5494	175	20	,	,	PUNCT
ejpam-5494	175	21	t	t	PROPN
ejpam-5494	175	22	)	)	PUNCT
ejpam-5494	175	23	=	=	PUNCT
ejpam-5494	175	24	k∑	k∑	PROPN
ejpam-5494	175	25	n=0	n=0	PROPN
ejpam-5494	175	26	bn(x	bn(x	X
ejpam-5494	175	27	)	)	PUNCT
ejpam-5494	175	28	tnγ	tnγ	NOUN
ejpam-5494	175	29	γ(nγ	γ(nγ	NOUN
ejpam-5494	175	30	+	+	CCONJ
ejpam-5494	175	31	1	1	NUM
ejpam-5494	175	32	)	)	PUNCT
ejpam-5494	175	33	.	.	PUNCT
ejpam-5494	176	1	the	the	DET
ejpam-5494	176	2	recurrence	recurrence	NOUN
ejpam-5494	176	3	relation	relation	NOUN
ejpam-5494	176	4	to	to	ADP
ejpam-5494	176	5	the	the	DET
ejpam-5494	176	6	above	above	ADJ
ejpam-5494	176	7	issue	issue	NOUN
ejpam-5494	176	8	is	be	AUX
ejpam-5494	176	9	u0(x	u0(x	NOUN
ejpam-5494	176	10	,	,	PUNCT
ejpam-5494	176	11	t	t	PROPN
ejpam-5494	176	12	)	)	PUNCT
ejpam-5494	176	13	=	=	SYM
ejpam-5494	177	1	ex	ex	X
ejpam-5494	177	2	,	,	PUNCT
ejpam-5494	177	3	w0(x	w0(x	PROPN
ejpam-5494	177	4	,	,	PUNCT
ejpam-5494	177	5	t	t	PROPN
ejpam-5494	177	6	)	)	PUNCT
ejpam-5494	177	7	=	=	SYM
ejpam-5494	178	1	e−x	e−x	NOUN
ejpam-5494	178	2	,	,	PUNCT
ejpam-5494	178	3	res1,k(x	res1,k(x	NOUN
ejpam-5494	178	4	,	,	PUNCT
ejpam-5494	178	5	t	t	PROPN
ejpam-5494	178	6	)	)	PUNCT
ejpam-5494	178	7	=	=	PUNCT
ejpam-5494	178	8	uk(x	uk(x	PROPN
ejpam-5494	178	9	,	,	PUNCT
ejpam-5494	178	10	t)−	t)−	PROPN
ejpam-5494	178	11	ex	ex	PRON
ejpam-5494	179	1	−	−	NOUN
ejpam-5494	179	2	s−1	s−1	PROPN
ejpam-5494	179	3	[	[	PUNCT
ejpam-5494	179	4	1	1	NUM
ejpam-5494	179	5	vγα	vγα	PROPN
ejpam-5494	179	6	s	s	X
ejpam-5494	179	7	[	[	PUNCT
ejpam-5494	179	8	−	−	PROPN
ejpam-5494	179	9	w2	w2	PROPN
ejpam-5494	179	10	k−1(uk−1	k−1(uk−1	PROPN
ejpam-5494	179	11	)	)	PUNCT
ejpam-5494	179	12	2	2	NUM
ejpam-5494	179	13	x	x	SYM
ejpam-5494	179	14	−	−	PROPN
ejpam-5494	179	15	uk−1	uk−1	ADJ
ejpam-5494	179	16	]	]	X
ejpam-5494	179	17	]	]	X
ejpam-5494	179	18	−	−	PUNCT
ejpam-5494	179	19	tγ	tγ	PROPN
ejpam-5494	179	20	γ(γ	γ(γ	PROPN
ejpam-5494	179	21	+	+	CCONJ
ejpam-5494	179	22	1	1	NUM
ejpam-5494	179	23	)	)	PUNCT
ejpam-5494	179	24	,	,	PUNCT
ejpam-5494	179	25	res2,k(x	res2,k(x	VERB
ejpam-5494	179	26	,	,	PUNCT
ejpam-5494	179	27	t	t	NOUN
ejpam-5494	179	28	)	)	PUNCT
ejpam-5494	179	29	=	=	SYM
ejpam-5494	179	30	wk(x	wk(x	NOUN
ejpam-5494	179	31	,	,	PUNCT
ejpam-5494	179	32	t)−	t)−	PROPN
ejpam-5494	179	33	e−x	e−x	NOUN
ejpam-5494	179	34	+	+	CCONJ
ejpam-5494	179	35	s−1	s−1	PROPN
ejpam-5494	179	36	[	[	PUNCT
ejpam-5494	179	37	1	1	NUM
ejpam-5494	179	38	vγα	vγα	NOUN
ejpam-5494	179	39	s	s	X
ejpam-5494	179	40	[	[	PUNCT
ejpam-5494	179	41	(	(	PUNCT
ejpam-5494	179	42	uk−1	uk−1	NOUN
ejpam-5494	179	43	)	)	PUNCT
ejpam-5494	179	44	2(wk−1	2(wk−1	NUM
ejpam-5494	179	45	)	)	PUNCT
ejpam-5494	179	46	2	2	NUM
ejpam-5494	179	47	x	x	SYM
ejpam-5494	179	48	−	−	NOUN
ejpam-5494	180	1	wk−1	wk−1	NOUN
ejpam-5494	180	2	]	]	X
ejpam-5494	180	3	]	]	X
ejpam-5494	180	4	−	−	PUNCT
ejpam-5494	180	5	tγ	tγ	PROPN
ejpam-5494	180	6	γ(γ	γ(γ	PROPN
ejpam-5494	180	7	+	+	CCONJ
ejpam-5494	180	8	1	1	NUM
ejpam-5494	180	9	)	)	PUNCT
ejpam-5494	180	10	,	,	PUNCT
ejpam-5494	181	1	k	k	PROPN
ejpam-5494	182	1	⩾	⩾	NOUN
ejpam-5494	183	1	1	1	X
ejpam-5494	183	2	.	.	X
ejpam-5494	183	3	for	for	ADP
ejpam-5494	183	4	k	k	PROPN
ejpam-5494	183	5	=	=	SYM
ejpam-5494	183	6	1	1	X
ejpam-5494	183	7	.	.	PUNCT
ejpam-5494	184	1	the	the	DET
ejpam-5494	184	2	first	first	ADJ
ejpam-5494	184	3	-	-	PUNCT
ejpam-5494	184	4	order	order	NOUN
ejpam-5494	184	5	approximate	approximate	ADJ
ejpam-5494	184	6	solution	solution	NOUN
ejpam-5494	184	7	is	be	AUX
ejpam-5494	184	8	assumed	assume	VERB
ejpam-5494	184	9	u1(x	u1(x	PROPN
ejpam-5494	184	10	,	,	PUNCT
ejpam-5494	184	11	t	t	PROPN
ejpam-5494	184	12	)	)	PUNCT
ejpam-5494	184	13	=	=	SYM
ejpam-5494	185	1	ex	ex	X
ejpam-5494	185	2	+	+	NOUN
ejpam-5494	185	3	a1(x	a1(x	NOUN
ejpam-5494	185	4	)	)	PUNCT
ejpam-5494	185	5	tγ	tγ	NOUN
ejpam-5494	185	6	γ(γ	γ(γ	PROPN
ejpam-5494	185	7	+	+	CCONJ
ejpam-5494	185	8	1	1	NUM
ejpam-5494	185	9	)	)	PUNCT
ejpam-5494	185	10	,	,	PUNCT
ejpam-5494	185	11	w1(x	w1(x	PROPN
ejpam-5494	185	12	,	,	PUNCT
ejpam-5494	185	13	t	t	PROPN
ejpam-5494	185	14	)	)	PUNCT
ejpam-5494	186	1	=	=	SYM
ejpam-5494	186	2	e−x	e−x	PROPN
ejpam-5494	186	3	+	+	CCONJ
ejpam-5494	186	4	b1(x	b1(x	NOUN
ejpam-5494	186	5	)	)	PUNCT
ejpam-5494	186	6	tγ	tγ	NOUN
ejpam-5494	186	7	γ(γ	γ(γ	PROPN
ejpam-5494	186	8	+	+	CCONJ
ejpam-5494	186	9	1	1	NUM
ejpam-5494	186	10	)	)	PUNCT
ejpam-5494	186	11	.	.	PUNCT
ejpam-5494	187	1	substituting	substitute	VERB
ejpam-5494	187	2	into	into	ADP
ejpam-5494	187	3	the	the	DET
ejpam-5494	187	4	above	above	ADJ
ejpam-5494	187	5	iteration	iteration	NOUN
ejpam-5494	187	6	yields	yield	NOUN
ejpam-5494	187	7	res1,1(x	res1,1(x	PROPN
ejpam-5494	187	8	,	,	PUNCT
ejpam-5494	187	9	t	t	PROPN
ejpam-5494	187	10	)	)	PUNCT
ejpam-5494	187	11	=	=	PUNCT
ejpam-5494	187	12	u1(x	u1(x	PROPN
ejpam-5494	187	13	,	,	PUNCT
ejpam-5494	187	14	t)−	t)−	PROPN
ejpam-5494	187	15	ex	ex	PRON
ejpam-5494	187	16	−	−	NOUN
ejpam-5494	187	17	s−1	s−1	PROPN
ejpam-5494	187	18	[	[	PUNCT
ejpam-5494	187	19	1	1	NUM
ejpam-5494	187	20	vγα	vγα	PROPN
ejpam-5494	187	21	s	s	X
ejpam-5494	187	22	[	[	PUNCT
ejpam-5494	187	23	−	−	PROPN
ejpam-5494	187	24	w2	w2	PROPN
ejpam-5494	187	25	0(u0	0(u0	PROPN
ejpam-5494	187	26	)	)	PUNCT
ejpam-5494	187	27	2	2	NUM
ejpam-5494	187	28	x	x	SYM
ejpam-5494	187	29	−	−	NOUN
ejpam-5494	187	30	u0	u0	ADJ
ejpam-5494	187	31	]	]	X
ejpam-5494	187	32	]	]	X
ejpam-5494	187	33	−	−	PUNCT
ejpam-5494	187	34	tγ	tγ	PROPN
ejpam-5494	187	35	γ(γ	γ(γ	PROPN
ejpam-5494	187	36	+	+	CCONJ
ejpam-5494	187	37	1	1	NUM
ejpam-5494	187	38	)	)	PUNCT
ejpam-5494	187	39	,	,	PUNCT
ejpam-5494	187	40	=	=	PUNCT
ejpam-5494	187	41	a1(x	a1(x	NOUN
ejpam-5494	187	42	)	)	PUNCT
ejpam-5494	187	43	tγ	tγ	NOUN
ejpam-5494	187	44	γ(γ	γ(γ	PROPN
ejpam-5494	187	45	+	+	CCONJ
ejpam-5494	187	46	1	1	X
ejpam-5494	187	47	)	)	PUNCT
ejpam-5494	187	48	+	+	CCONJ
ejpam-5494	187	49	ex	ex	PRON
ejpam-5494	187	50	tγ	tγ	NOUN
ejpam-5494	187	51	γ(γ	γ(γ	PROPN
ejpam-5494	187	52	+	+	CCONJ
ejpam-5494	187	53	1	1	NUM
ejpam-5494	187	54	)	)	PUNCT
ejpam-5494	187	55	,	,	PUNCT
ejpam-5494	187	56	res2,1(x	res2,1(x	NOUN
ejpam-5494	187	57	,	,	PUNCT
ejpam-5494	187	58	t	t	NOUN
ejpam-5494	187	59	)	)	PUNCT
ejpam-5494	187	60	=	=	SYM
ejpam-5494	187	61	w1(x	w1(x	PROPN
ejpam-5494	187	62	,	,	PUNCT
ejpam-5494	187	63	t)−	t)−	PROPN
ejpam-5494	187	64	e−x	e−x	NOUN
ejpam-5494	187	65	+	+	X
ejpam-5494	187	66	s−1	s−1	PROPN
ejpam-5494	187	67	[	[	PUNCT
ejpam-5494	187	68	1	1	NUM
ejpam-5494	187	69	vγα	vγα	NOUN
ejpam-5494	187	70	s	s	X
ejpam-5494	187	71	[	[	PUNCT
ejpam-5494	187	72	(	(	PUNCT
ejpam-5494	187	73	u0	u0	ADJ
ejpam-5494	187	74	)	)	PUNCT
ejpam-5494	187	75	2(w0	2(w0	NUM
ejpam-5494	187	76	)	)	PUNCT
ejpam-5494	187	77	2	2	NUM
ejpam-5494	187	78	x	x	SYM
ejpam-5494	187	79	−	−	PROPN
ejpam-5494	187	80	w0	w0	PROPN
ejpam-5494	187	81	]	]	X
ejpam-5494	187	82	]	]	X
ejpam-5494	187	83	−	−	PUNCT
ejpam-5494	187	84	tγ	tγ	PROPN
ejpam-5494	187	85	γ(γ	γ(γ	PROPN
ejpam-5494	187	86	+	+	CCONJ
ejpam-5494	187	87	1	1	NUM
ejpam-5494	187	88	)	)	PUNCT
ejpam-5494	187	89	,	,	PUNCT
ejpam-5494	187	90	=	=	PUNCT
ejpam-5494	187	91	b1(x	b1(x	NOUN
ejpam-5494	187	92	)	)	PUNCT
ejpam-5494	187	93	tγ	tγ	NOUN
ejpam-5494	187	94	γ(γ	γ(γ	PROPN
ejpam-5494	188	1	+	+	CCONJ
ejpam-5494	188	2	1	1	X
ejpam-5494	188	3	)	)	PUNCT
ejpam-5494	188	4	−	−	PROPN
ejpam-5494	188	5	ex	ex	PRON
ejpam-5494	188	6	tγ	tγ	PROPN
ejpam-5494	188	7	γ(γ	γ(γ	PROPN
ejpam-5494	188	8	+	+	CCONJ
ejpam-5494	188	9	1	1	NUM
ejpam-5494	188	10	)	)	PUNCT
ejpam-5494	188	11	.	.	PUNCT
ejpam-5494	189	1	figure	figure	VERB
ejpam-5494	189	2	1	1	NUM
ejpam-5494	189	3	:	:	PUNCT
ejpam-5494	189	4	subplot	subplot	NOUN
ejpam-5494	189	5	(	(	PUNCT
ejpam-5494	189	6	a	a	PRON
ejpam-5494	189	7	)	)	PUNCT
ejpam-5494	189	8	displays	display	VERB
ejpam-5494	189	9	the	the	DET
ejpam-5494	189	10	approximate	approximate	ADJ
ejpam-5494	189	11	solution	solution	NOUN
ejpam-5494	189	12	u5(x	u5(x	PROPN
ejpam-5494	189	13	,	,	PUNCT
ejpam-5494	189	14	t	t	PROPN
ejpam-5494	189	15	)	)	PUNCT
ejpam-5494	189	16	,	,	PUNCT
ejpam-5494	189	17	and	and	CCONJ
ejpam-5494	189	18	subplot	subplot	NOUN
ejpam-5494	189	19	(	(	PUNCT
ejpam-5494	189	20	b	b	NOUN
ejpam-5494	189	21	)	)	PUNCT
ejpam-5494	189	22	presents	present	VERB
ejpam-5494	189	23	the	the	DET
ejpam-5494	189	24	approximate	approximate	ADJ
ejpam-5494	189	25	solution	solution	NOUN
ejpam-5494	189	26	w5(x	w5(x	PROPN
ejpam-5494	189	27	,	,	PUNCT
ejpam-5494	189	28	t	t	PROPN
ejpam-5494	189	29	)	)	PUNCT
ejpam-5494	189	30	for	for	ADP
ejpam-5494	189	31	example	example	NOUN
ejpam-5494	189	32	1	1	NUM
ejpam-5494	189	33	with	with	ADP
ejpam-5494	189	34	different	different	ADJ
ejpam-5494	189	35	γ	γ	NOUN
ejpam-5494	189	36	values	value	NOUN
ejpam-5494	189	37	at	at	ADP
ejpam-5494	189	38	x	x	X
ejpam-5494	189	39	=	=	SYM
ejpam-5494	189	40	0.5	0.5	NUM
ejpam-5494	189	41	.	.	PUNCT
ejpam-5494	190	1	p.	p.	NOUN
ejpam-5494	190	2	pue	pue	NOUN
ejpam-5494	190	3	-	-	PUNCT
ejpam-5494	190	4	on	on	ADP
ejpam-5494	190	5	/	/	SYM
ejpam-5494	190	6	eur	eur	NOUN
ejpam-5494	190	7	.	.	PUNCT
ejpam-5494	191	1	j.	j.	PROPN
ejpam-5494	191	2	pure	pure	PROPN
ejpam-5494	191	3	appl	appl	PROPN
ejpam-5494	191	4	.	.	PROPN
ejpam-5494	191	5	math	math	PROPN
ejpam-5494	191	6	,	,	PUNCT
ejpam-5494	191	7	17	17	NUM
ejpam-5494	191	8	(	(	PUNCT
ejpam-5494	191	9	4	4	NUM
ejpam-5494	191	10	)	)	PUNCT
ejpam-5494	191	11	(	(	PUNCT
ejpam-5494	191	12	2024	2024	NUM
ejpam-5494	191	13	)	)	PUNCT
ejpam-5494	191	14	,	,	PUNCT
ejpam-5494	191	15	3826	3826	NUM
ejpam-5494	191	16	-	-	SYM
ejpam-5494	191	17	3846	3846	NUM
ejpam-5494	191	18	3834	3834	NUM
ejpam-5494	191	19	figure	figure	NOUN
ejpam-5494	191	20	2	2	NUM
ejpam-5494	191	21	:	:	PUNCT
ejpam-5494	191	22	the	the	DET
ejpam-5494	191	23	graphics	graphic	NOUN
ejpam-5494	191	24	represent	represent	VERB
ejpam-5494	191	25	the	the	DET
ejpam-5494	191	26	approximate	approximate	ADJ
ejpam-5494	191	27	solution	solution	NOUN
ejpam-5494	191	28	u5(x	u5(x	PROPN
ejpam-5494	191	29	,	,	PUNCT
ejpam-5494	191	30	t	t	PROPN
ejpam-5494	191	31	)	)	PUNCT
ejpam-5494	191	32	with	with	ADP
ejpam-5494	191	33	different	different	ADJ
ejpam-5494	191	34	γ	γ	NOUN
ejpam-5494	191	35	values	value	NOUN
ejpam-5494	191	36	:	:	PUNCT
ejpam-5494	191	37	(	(	PUNCT
ejpam-5494	191	38	a	a	X
ejpam-5494	191	39	)	)	PUNCT
ejpam-5494	191	40	γ	γ	NOUN
ejpam-5494	191	41	=	=	SYM
ejpam-5494	191	42	0.6	0.6	NUM
ejpam-5494	191	43	,	,	PUNCT
ejpam-5494	191	44	(	(	PUNCT
ejpam-5494	191	45	b	b	X
ejpam-5494	191	46	)	)	PUNCT
ejpam-5494	191	47	γ	γ	NOUN
ejpam-5494	191	48	=	=	NUM
ejpam-5494	191	49	0.8	0.8	NUM
ejpam-5494	191	50	,	,	PUNCT
ejpam-5494	191	51	(	(	PUNCT
ejpam-5494	191	52	c	c	X
ejpam-5494	191	53	)	)	PUNCT
ejpam-5494	191	54	γ	γ	NOUN
ejpam-5494	191	55	=	=	SYM
ejpam-5494	191	56	1	1	NUM
ejpam-5494	191	57	,	,	PUNCT
ejpam-5494	191	58	and	and	CCONJ
ejpam-5494	191	59	(	(	PUNCT
ejpam-5494	191	60	d	d	X
ejpam-5494	191	61	)	)	PUNCT
ejpam-5494	191	62	the	the	DET
ejpam-5494	191	63	exact	exact	ADJ
ejpam-5494	191	64	solution	solution	NOUN
ejpam-5494	191	65	for	for	ADP
ejpam-5494	191	66	example	example	NOUN
ejpam-5494	191	67	1	1	NUM
ejpam-5494	191	68	.	.	X
ejpam-5494	191	69	figure	figure	VERB
ejpam-5494	191	70	3	3	NUM
ejpam-5494	191	71	:	:	PUNCT
ejpam-5494	191	72	the	the	DET
ejpam-5494	191	73	graphics	graphic	NOUN
ejpam-5494	191	74	represent	represent	VERB
ejpam-5494	191	75	the	the	DET
ejpam-5494	191	76	approximate	approximate	ADJ
ejpam-5494	191	77	solution	solution	NOUN
ejpam-5494	191	78	w5(x	w5(x	PROPN
ejpam-5494	191	79	,	,	PUNCT
ejpam-5494	191	80	t	t	PROPN
ejpam-5494	191	81	)	)	PUNCT
ejpam-5494	191	82	with	with	ADP
ejpam-5494	191	83	different	different	ADJ
ejpam-5494	191	84	γ	γ	NOUN
ejpam-5494	191	85	values	value	NOUN
ejpam-5494	191	86	:	:	PUNCT
ejpam-5494	191	87	(	(	PUNCT
ejpam-5494	191	88	a	a	X
ejpam-5494	191	89	)	)	PUNCT
ejpam-5494	191	90	γ	γ	NOUN
ejpam-5494	191	91	=	=	SYM
ejpam-5494	191	92	0.6	0.6	NUM
ejpam-5494	191	93	,	,	PUNCT
ejpam-5494	191	94	(	(	PUNCT
ejpam-5494	191	95	b	b	X
ejpam-5494	191	96	)	)	PUNCT
ejpam-5494	191	97	γ	γ	NOUN
ejpam-5494	191	98	=	=	NUM
ejpam-5494	191	99	0.8	0.8	NUM
ejpam-5494	191	100	,	,	PUNCT
ejpam-5494	191	101	(	(	PUNCT
ejpam-5494	191	102	c	c	X
ejpam-5494	191	103	)	)	PUNCT
ejpam-5494	191	104	γ	γ	NOUN
ejpam-5494	191	105	=	=	SYM
ejpam-5494	191	106	1	1	NUM
ejpam-5494	191	107	,	,	PUNCT
ejpam-5494	191	108	and	and	CCONJ
ejpam-5494	191	109	(	(	PUNCT
ejpam-5494	191	110	d	d	X
ejpam-5494	191	111	)	)	PUNCT
ejpam-5494	191	112	the	the	DET
ejpam-5494	191	113	exact	exact	ADJ
ejpam-5494	191	114	solution	solution	NOUN
ejpam-5494	191	115	for	for	ADP
ejpam-5494	191	116	example	example	NOUN
ejpam-5494	191	117	1	1	NUM
ejpam-5494	191	118	.	.	PUNCT
ejpam-5494	192	1	p.	p.	NOUN
ejpam-5494	192	2	pue	pue	NOUN
ejpam-5494	192	3	-	-	PUNCT
ejpam-5494	192	4	on	on	ADP
ejpam-5494	192	5	/	/	SYM
ejpam-5494	192	6	eur	eur	NOUN
ejpam-5494	192	7	.	.	PUNCT
ejpam-5494	193	1	j.	j.	PROPN
ejpam-5494	193	2	pure	pure	PROPN
ejpam-5494	193	3	appl	appl	PROPN
ejpam-5494	193	4	.	.	PROPN
ejpam-5494	193	5	math	math	PROPN
ejpam-5494	193	6	,	,	PUNCT
ejpam-5494	193	7	17	17	NUM
ejpam-5494	193	8	(	(	PUNCT
ejpam-5494	193	9	4	4	NUM
ejpam-5494	193	10	)	)	PUNCT
ejpam-5494	193	11	(	(	PUNCT
ejpam-5494	193	12	2024	2024	NUM
ejpam-5494	193	13	)	)	PUNCT
ejpam-5494	193	14	,	,	PUNCT
ejpam-5494	193	15	3826	3826	NUM
ejpam-5494	193	16	-	-	SYM
ejpam-5494	193	17	3846	3846	NUM
ejpam-5494	193	18	3835	3835	NUM
ejpam-5494	193	19	using	use	VERB
ejpam-5494	193	20	the	the	DET
ejpam-5494	193	21	condition	condition	NOUN
ejpam-5494	193	22	(	(	PUNCT
ejpam-5494	193	23	9	9	NUM
ejpam-5494	193	24	)	)	PUNCT
ejpam-5494	193	25	with	with	ADP
ejpam-5494	193	26	k	k	PROPN
ejpam-5494	193	27	=	=	SYM
ejpam-5494	193	28	1	1	NUM
ejpam-5494	193	29	,	,	PUNCT
ejpam-5494	193	30	t−γres1,1(x	t−γres1,1(x	NOUN
ejpam-5494	193	31	,	,	PUNCT
ejpam-5494	193	32	t	t	PROPN
ejpam-5494	193	33	)	)	PUNCT
ejpam-5494	193	34	∣∣	∣∣	NUM
ejpam-5494	193	35	t=0	t=0	X
ejpam-5494	194	1	=	=	SYM
ejpam-5494	194	2	0	0	NUM
ejpam-5494	194	3	,	,	PUNCT
ejpam-5494	194	4	t−γres2,1(x	t−γres2,1(x	NOUN
ejpam-5494	194	5	,	,	PUNCT
ejpam-5494	194	6	t	t	PROPN
ejpam-5494	194	7	)	)	PUNCT
ejpam-5494	194	8	∣∣	∣∣	NUM
ejpam-5494	194	9	t=0	t=0	X
ejpam-5494	194	10	=	=	SYM
ejpam-5494	194	11	0	0	NUM
ejpam-5494	194	12	,	,	PUNCT
ejpam-5494	194	13	produces	produce	VERB
ejpam-5494	194	14	the	the	DET
ejpam-5494	194	15	coefficients	coefficient	NOUN
ejpam-5494	194	16	that	that	PRON
ejpam-5494	194	17	are	be	AUX
ejpam-5494	194	18	a1(x	a1(x	PRON
ejpam-5494	194	19	)	)	PUNCT
ejpam-5494	194	20	=	=	SYM
ejpam-5494	194	21	−e−x	−e−x	PROPN
ejpam-5494	194	22	and	and	CCONJ
ejpam-5494	194	23	b1(x	b1(x	NOUN
ejpam-5494	194	24	)	)	PUNCT
ejpam-5494	194	25	=	=	SYM
ejpam-5494	195	1	ex	ex	X
ejpam-5494	195	2	.	.	NOUN
ejpam-5494	195	3	as	as	ADP
ejpam-5494	195	4	a	a	DET
ejpam-5494	195	5	result	result	NOUN
ejpam-5494	195	6	,	,	PUNCT
ejpam-5494	195	7	the	the	DET
ejpam-5494	195	8	firstorder	firstorder	NOUN
ejpam-5494	195	9	truncated	truncate	VERB
ejpam-5494	195	10	series	series	NOUN
ejpam-5494	195	11	solution	solution	NOUN
ejpam-5494	195	12	is	be	AUX
ejpam-5494	195	13	u1(x	u1(x	PROPN
ejpam-5494	195	14	,	,	PUNCT
ejpam-5494	195	15	t	t	PROPN
ejpam-5494	195	16	)	)	PUNCT
ejpam-5494	195	17	=	=	SYM
ejpam-5494	196	1	ex	ex	PRON
ejpam-5494	197	1	−	−	X
ejpam-5494	197	2	ex	ex	PUNCT
ejpam-5494	197	3	tγ	tγ	PROPN
ejpam-5494	197	4	γ(γ	γ(γ	PROPN
ejpam-5494	197	5	+	+	CCONJ
ejpam-5494	197	6	1	1	NUM
ejpam-5494	197	7	)	)	PUNCT
ejpam-5494	197	8	,	,	PUNCT
ejpam-5494	197	9	w1(x	w1(x	PROPN
ejpam-5494	197	10	,	,	PUNCT
ejpam-5494	197	11	t	t	PROPN
ejpam-5494	197	12	)	)	PUNCT
ejpam-5494	197	13	=	=	SYM
ejpam-5494	198	1	e−x	e−x	PROPN
ejpam-5494	198	2	+	+	NUM
ejpam-5494	198	3	e−x	e−x	PROPN
ejpam-5494	198	4	tγ	tγ	PROPN
ejpam-5494	198	5	γ(γ	γ(γ	PROPN
ejpam-5494	198	6	+	+	CCONJ
ejpam-5494	198	7	1	1	NUM
ejpam-5494	198	8	)	)	PUNCT
ejpam-5494	198	9	.	.	PUNCT
ejpam-5494	199	1	table	table	NOUN
ejpam-5494	199	2	1	1	NUM
ejpam-5494	199	3	:	:	PUNCT
ejpam-5494	199	4	comparison	comparison	NOUN
ejpam-5494	199	5	of	of	ADP
ejpam-5494	199	6	the	the	DET
ejpam-5494	199	7	approximate	approximate	ADJ
ejpam-5494	199	8	solution	solution	NOUN
ejpam-5494	199	9	u5(x	u5(x	PROPN
ejpam-5494	199	10	,	,	PUNCT
ejpam-5494	199	11	t	t	PROPN
ejpam-5494	199	12	)	)	PUNCT
ejpam-5494	199	13	for	for	ADP
ejpam-5494	199	14	γ	γ	X
ejpam-5494	199	15	=	=	SYM
ejpam-5494	199	16	1	1	NUM
ejpam-5494	199	17	and	and	CCONJ
ejpam-5494	199	18	error	error	NOUN
ejpam-5494	199	19	analysis	analysis	NOUN
ejpam-5494	199	20	in	in	ADP
ejpam-5494	199	21	example	example	NOUN
ejpam-5494	199	22	1	1	NUM
ejpam-5494	199	23	using	use	VERB
ejpam-5494	199	24	different	different	ADJ
ejpam-5494	199	25	t	t	PROPN
ejpam-5494	199	26	,	,	PUNCT
ejpam-5494	199	27	x	x	NOUN
ejpam-5494	199	28	values	value	NOUN
ejpam-5494	199	29	.	.	PUNCT
ejpam-5494	200	1	t	t	X
ejpam-5494	200	2	x	x	SYM
ejpam-5494	200	3	u5(x	u5(x	PROPN
ejpam-5494	200	4	,	,	PUNCT
ejpam-5494	200	5	t	t	PROPN
ejpam-5494	200	6	)	)	PUNCT
ejpam-5494	200	7	exact	exact	PROPN
ejpam-5494	200	8	soln	soln	NOUN
ejpam-5494	200	9	.	.	PUNCT
ejpam-5494	201	1	abs.error	abs.error	PROPN
ejpam-5494	202	1	(	(	PUNCT
ejpam-5494	202	2	srpsm	srpsm	ADJ
ejpam-5494	202	3	)	)	PUNCT
ejpam-5494	202	4	abs.error	abs.error	PROPN
ejpam-5494	202	5	(	(	PUNCT
ejpam-5494	202	6	lrpsm	lrpsm	PROPN
ejpam-5494	202	7	)	)	PUNCT
ejpam-5494	203	1	[	[	X
ejpam-5494	203	2	4	4	X
ejpam-5494	203	3	]	]	SYM
ejpam-5494	203	4	0.2	0.2	NUM
ejpam-5494	203	5	1.105170916	1.105170916	NUM
ejpam-5494	203	6	1.105170918	1.105170918	NUM
ejpam-5494	203	7	2×	2×	NUM
ejpam-5494	203	8	10−9	10−9	NUM
ejpam-5494	203	9	2×	2×	NUM
ejpam-5494	203	10	10−9	10−9	NUM
ejpam-5494	203	11	0.4	0.4	NUM
ejpam-5494	203	12	1.349858806	1.349858806	NUM
ejpam-5494	203	13	1.349858808	1.349858808	NUM
ejpam-5494	203	14	2×	2×	NUM
ejpam-5494	203	15	10−9	10−9	NUM
ejpam-5494	203	16	2×	2×	NUM
ejpam-5494	203	17	10−9	10−9	NUM
ejpam-5494	203	18	0.1	0.1	NUM
ejpam-5494	203	19	0.6	0.6	NUM
ejpam-5494	203	20	1.648721268	1.648721268	NUM
ejpam-5494	203	21	1.648721271	1.648721271	NUM
ejpam-5494	203	22	3×	3×	NUM
ejpam-5494	203	23	10−9	10−9	NUM
ejpam-5494	203	24	3×	3×	NUM
ejpam-5494	203	25	10−9	10−9	NUM
ejpam-5494	203	26	0.8	0.8	NUM
ejpam-5494	203	27	2.013752704	2.013752704	NUM
ejpam-5494	203	28	2.013752707	2.013752707	NUM
ejpam-5494	203	29	3×	3×	NUM
ejpam-5494	203	30	10−9	10−9	NUM
ejpam-5494	203	31	3×	3×	NUM
ejpam-5494	203	32	10−9	10−9	NUM
ejpam-5494	203	33	1.0	1.0	NUM
ejpam-5494	203	34	2.459603107	2.459603107	NUM
ejpam-5494	203	35	2.459603111	2.459603111	NUM
ejpam-5494	203	36	4×	4×	NOUN
ejpam-5494	203	37	10−9	10−9	NUM
ejpam-5494	203	38	4×	4×	NOUN
ejpam-5494	203	39	10−9	10−9	NUM
ejpam-5494	203	40	0.2	0.2	NUM
ejpam-5494	203	41	0.9512290245	0.9512290245	NUM
ejpam-5494	203	42	0.9512294245	0.9512294245	NUM
ejpam-5494	203	43	4×	4×	NOUN
ejpam-5494	203	44	10−7	10−7	NUM
ejpam-5494	203	45	4×	4×	NOUN
ejpam-5494	203	46	10−7	10−7	NUM
ejpam-5494	203	47	0.4	0.4	NUM
ejpam-5494	203	48	1.161833755	1.161833755	NUM
ejpam-5494	203	49	1.161834243	1.161834243	NUM
ejpam-5494	203	50	4.88×	4.88×	NUM
ejpam-5494	203	51	10−7	10−7	NUM
ejpam-5494	203	52	4.88×	4.88×	NUM
ejpam-5494	203	53	10−7	10−7	NUM
ejpam-5494	203	54	0.25	0.25	NUM
ejpam-5494	203	55	0.6	0.6	NUM
ejpam-5494	203	56	1.419066952	1.419066952	NUM
ejpam-5494	203	57	1.419067549	1.419067549	NUM
ejpam-5494	203	58	5.97×	5.97×	NUM
ejpam-5494	203	59	10−7	10−7	NUM
ejpam-5494	203	60	5.97×	5.97×	NUM
ejpam-5494	203	61	10−7	10−7	NUM
ejpam-5494	203	62	0.8	0.8	NUM
ejpam-5494	203	63	1.733252289	1.733252289	NUM
ejpam-5494	203	64	1.733253018	1.733253018	NUM
ejpam-5494	203	65	7.29×	7.29×	NUM
ejpam-5494	203	66	10−7	10−7	NUM
ejpam-5494	203	67	7.29×	7.29×	NUM
ejpam-5494	203	68	10−7	10−7	NUM
ejpam-5494	203	69	1.0	1.0	NUM
ejpam-5494	203	70	2.116999126	2.116999126	NUM
ejpam-5494	203	71	2.117000017	2.117000017	NUM
ejpam-5494	203	72	8.90×	8.90×	NUM
ejpam-5494	203	73	10−7	10−7	NUM
ejpam-5494	203	74	8.90×	8.90×	NUM
ejpam-5494	203	75	10−7	10−7	NUM
ejpam-5494	203	76	table	table	NOUN
ejpam-5494	203	77	2	2	NUM
ejpam-5494	203	78	:	:	PUNCT
ejpam-5494	203	79	comparison	comparison	NOUN
ejpam-5494	203	80	of	of	ADP
ejpam-5494	203	81	the	the	DET
ejpam-5494	203	82	approximate	approximate	ADJ
ejpam-5494	203	83	solution	solution	NOUN
ejpam-5494	203	84	w5(x	w5(x	PROPN
ejpam-5494	203	85	,	,	PUNCT
ejpam-5494	203	86	t	t	PROPN
ejpam-5494	203	87	)	)	PUNCT
ejpam-5494	203	88	for	for	ADP
ejpam-5494	203	89	γ	γ	X
ejpam-5494	203	90	=	=	SYM
ejpam-5494	203	91	1	1	NUM
ejpam-5494	203	92	and	and	CCONJ
ejpam-5494	203	93	error	error	NOUN
ejpam-5494	203	94	analysis	analysis	NOUN
ejpam-5494	203	95	in	in	ADP
ejpam-5494	203	96	example	example	NOUN
ejpam-5494	203	97	1	1	NUM
ejpam-5494	203	98	using	use	VERB
ejpam-5494	203	99	different	different	ADJ
ejpam-5494	203	100	x	x	NOUN
ejpam-5494	203	101	,	,	PUNCT
ejpam-5494	203	102	t	t	PROPN
ejpam-5494	203	103	values	value	NOUN
ejpam-5494	203	104	.	.	PUNCT
ejpam-5494	204	1	t	t	X
ejpam-5494	204	2	x	x	X
ejpam-5494	204	3	w5(x	w5(x	PROPN
ejpam-5494	204	4	,	,	PUNCT
ejpam-5494	204	5	t	t	PROPN
ejpam-5494	204	6	)	)	PUNCT
ejpam-5494	204	7	exact	exact	PROPN
ejpam-5494	204	8	soln	soln	NOUN
ejpam-5494	204	9	.	.	PUNCT
ejpam-5494	205	1	abs.error	abs.error	PROPN
ejpam-5494	206	1	(	(	PUNCT
ejpam-5494	206	2	srpsm	srpsm	ADJ
ejpam-5494	206	3	)	)	PUNCT
ejpam-5494	206	4	abs.error	abs.error	PROPN
ejpam-5494	206	5	(	(	PUNCT
ejpam-5494	206	6	lrpsm	lrpsm	PROPN
ejpam-5494	206	7	)	)	PUNCT
ejpam-5494	207	1	[	[	X
ejpam-5494	207	2	4	4	X
ejpam-5494	207	3	]	]	SYM
ejpam-5494	207	4	0.2	0.2	NUM
ejpam-5494	207	5	0.9048374172	0.9048374172	NUM
ejpam-5494	207	6	0.9048374180	0.9048374180	NUM
ejpam-5494	207	7	8×	8×	NUM
ejpam-5494	207	8	10−10	10−10	NUM
ejpam-5494	207	9	8×	8×	NUM
ejpam-5494	207	10	10−10	10−10	NUM
ejpam-5494	207	11	0.4	0.4	NUM
ejpam-5494	207	12	0.7408182199	0.7408182199	NUM
ejpam-5494	207	13	0.7408182207	0.7408182207	NUM
ejpam-5494	207	14	8×	8×	ADP
ejpam-5494	207	15	10−10	10−10	NUM
ejpam-5494	207	16	8×	8×	NUM
ejpam-5494	207	17	10−10	10−10	NUM
ejpam-5494	207	18	0.1	0.1	NUM
ejpam-5494	207	19	0.6	0.6	NUM
ejpam-5494	207	20	0.6065306591	0.6065306591	NUM
ejpam-5494	207	21	0.6065306597	0.6065306597	NUM
ejpam-5494	207	22	6×	6×	NUM
ejpam-5494	207	23	10−10	10−10	NUM
ejpam-5494	207	24	6×	6×	NOUN
ejpam-5494	207	25	10−10	10−10	NUM
ejpam-5494	207	26	0.8	0.8	NUM
ejpam-5494	207	27	0.4965853033	0.4965853033	NUM
ejpam-5494	207	28	0.4965853038	0.4965853038	NUM
ejpam-5494	207	29	5×	5×	NOUN
ejpam-5494	207	30	10−10	10−10	NUM
ejpam-5494	207	31	5×	5×	NOUN
ejpam-5494	207	32	10−10	10−10	NUM
ejpam-5494	207	33	1.0	1.0	NUM
ejpam-5494	207	34	0.4065696594	0.4065696594	NUM
ejpam-5494	207	35	0.4065696597	0.4065696597	NUM
ejpam-5494	207	36	3×	3×	NUM
ejpam-5494	207	37	10−10	10−10	NUM
ejpam-5494	207	38	3×	3×	NUM
ejpam-5494	207	39	10−10	10−10	NUM
ejpam-5494	207	40	0.2	0.2	NUM
ejpam-5494	207	41	1.051270808	1.051270808	NUM
ejpam-5494	207	42	1.051271096	1.051271096	NUM
ejpam-5494	207	43	2.88×	2.88×	NUM
ejpam-5494	207	44	10−7	10−7	NUM
ejpam-5494	207	45	2.88×	2.88×	NUM
ejpam-5494	207	46	10−7	10−7	NUM
ejpam-5494	207	47	0.4	0.4	NUM
ejpam-5494	207	48	0.8607077406	0.8607077406	NUM
ejpam-5494	207	49	0.8607079764	0.8607079764	NUM
ejpam-5494	207	50	2.358×	2.358×	NUM
ejpam-5494	207	51	10−7	10−7	NUM
ejpam-5494	207	52	2.358×	2.358×	NUM
ejpam-5494	207	53	10−7	10−7	NUM
ejpam-5494	207	54	0.25	0.25	NUM
ejpam-5494	207	55	0.6	0.6	NUM
ejpam-5494	207	56	0.7046878967	0.7046878967	NUM
ejpam-5494	207	57	0.7046880897	0.7046880897	NUM
ejpam-5494	207	58	1.93×	1.93×	NUM
ejpam-5494	207	59	10−7	10−7	NUM
ejpam-5494	207	60	1.93×	1.93×	NUM
ejpam-5494	207	61	10−7	10−7	NUM
ejpam-5494	207	62	0.8	0.8	NUM
ejpam-5494	207	63	0.5769496523	0.5769496523	NUM
ejpam-5494	207	64	0.5769498104	0.5769498104	NUM
ejpam-5494	207	65	1.581×	1.581×	NUM
ejpam-5494	207	66	10−7	10−7	NUM
ejpam-5494	207	67	1.581×	1.581×	NUM
ejpam-5494	207	68	10−7	10−7	NUM
ejpam-5494	207	69	1.0	1.0	NUM
ejpam-5494	207	70	0.4723664234	0.4723664234	NUM
ejpam-5494	207	71	0.4723665527	0.4723665527	NUM
ejpam-5494	207	72	1.293×	1.293×	NUM
ejpam-5494	207	73	10−7	10−7	NUM
ejpam-5494	207	74	1.293×	1.293×	NUM
ejpam-5494	207	75	10−7	10−7	NUM
ejpam-5494	207	76	for	for	ADP
ejpam-5494	207	77	k	k	PROPN
ejpam-5494	207	78	⩾	⩾	PROPN
ejpam-5494	207	79	2	2	X
ejpam-5494	207	80	.	.	PUNCT
ejpam-5494	207	81	by	by	ADP
ejpam-5494	207	82	employing	employ	VERB
ejpam-5494	207	83	the	the	DET
ejpam-5494	207	84	offered	offer	VERB
ejpam-5494	207	85	procedure	procedure	NOUN
ejpam-5494	207	86	and	and	CCONJ
ejpam-5494	207	87	condition	condition	NOUN
ejpam-5494	207	88	(	(	PUNCT
ejpam-5494	207	89	9	9	NUM
ejpam-5494	207	90	)	)	PUNCT
ejpam-5494	207	91	,	,	PUNCT
ejpam-5494	207	92	the	the	DET
ejpam-5494	207	93	coefficients	coefficient	NOUN
ejpam-5494	207	94	of	of	ADP
ejpam-5494	207	95	the	the	DET
ejpam-5494	207	96	series	series	NOUN
ejpam-5494	207	97	solution	solution	NOUN
ejpam-5494	207	98	are	be	AUX
ejpam-5494	207	99	ak(x	ak(x	NOUN
ejpam-5494	207	100	)	)	PUNCT
ejpam-5494	208	1	=	=	SYM
ejpam-5494	208	2	(	(	PUNCT
ejpam-5494	208	3	−1)kex	−1)kex	PROPN
ejpam-5494	208	4	,	,	PUNCT
ejpam-5494	208	5	bk(x	bk(x	NOUN
ejpam-5494	208	6	)	)	PUNCT
ejpam-5494	208	7	=	=	SYM
ejpam-5494	208	8	e−x	e−x	NOUN
ejpam-5494	208	9	.	.	PUNCT
ejpam-5494	209	1	hence	hence	ADV
ejpam-5494	209	2	,	,	PUNCT
ejpam-5494	209	3	the	the	DET
ejpam-5494	209	4	k	k	ADJ
ejpam-5494	209	5	-	-	PUNCT
ejpam-5494	209	6	truncated	truncate	VERB
ejpam-5494	209	7	series	series	NOUN
ejpam-5494	209	8	solution	solution	NOUN
ejpam-5494	209	9	is	be	AUX
ejpam-5494	209	10	uk(x	uk(x	ADV
ejpam-5494	209	11	,	,	PUNCT
ejpam-5494	209	12	t	t	PROPN
ejpam-5494	209	13	)	)	PUNCT
ejpam-5494	209	14	=	=	PUNCT
ejpam-5494	210	1	k∑	k∑	PROPN
ejpam-5494	210	2	n=0	n=0	PRON
ejpam-5494	210	3	(	(	PUNCT
ejpam-5494	210	4	−1)nex	−1)nex	PROPN
ejpam-5494	210	5	tnγ	tnγ	PRON
ejpam-5494	210	6	γ(nγ	γ(nγ	NOUN
ejpam-5494	210	7	+	+	CCONJ
ejpam-5494	210	8	1	1	X
ejpam-5494	210	9	)	)	PUNCT
ejpam-5494	210	10	=	=	NOUN
ejpam-5494	211	1	ex	ex	X
ejpam-5494	211	2	k∑	k∑	PROPN
ejpam-5494	211	3	n=0	n=0	PROPN
ejpam-5494	211	4	(	(	PUNCT
ejpam-5494	211	5	−tγ)n	−tγ)n	NOUN
ejpam-5494	211	6	γ(nγ	γ(nγ	NOUN
ejpam-5494	211	7	+	+	CCONJ
ejpam-5494	211	8	1	1	NUM
ejpam-5494	211	9	)	)	PUNCT
ejpam-5494	211	10	,	,	PUNCT
ejpam-5494	211	11	p.	p.	NOUN
ejpam-5494	211	12	pue	pue	PROPN
ejpam-5494	211	13	-	-	PUNCT
ejpam-5494	211	14	on	on	ADP
ejpam-5494	211	15	/	/	SYM
ejpam-5494	211	16	eur	eur	NOUN
ejpam-5494	211	17	.	.	PUNCT
ejpam-5494	212	1	j.	j.	PROPN
ejpam-5494	212	2	pure	pure	PROPN
ejpam-5494	212	3	appl	appl	PROPN
ejpam-5494	212	4	.	.	PROPN
ejpam-5494	212	5	math	math	PROPN
ejpam-5494	212	6	,	,	PUNCT
ejpam-5494	212	7	17	17	NUM
ejpam-5494	212	8	(	(	PUNCT
ejpam-5494	212	9	4	4	NUM
ejpam-5494	212	10	)	)	PUNCT
ejpam-5494	212	11	(	(	PUNCT
ejpam-5494	212	12	2024	2024	NUM
ejpam-5494	212	13	)	)	PUNCT
ejpam-5494	212	14	,	,	PUNCT
ejpam-5494	212	15	3826	3826	NUM
ejpam-5494	212	16	-	-	SYM
ejpam-5494	212	17	3846	3846	NUM
ejpam-5494	212	18	3836	3836	NUM
ejpam-5494	212	19	wk(x	wk(x	NOUN
ejpam-5494	212	20	,	,	PUNCT
ejpam-5494	212	21	t	t	PROPN
ejpam-5494	212	22	)	)	PUNCT
ejpam-5494	212	23	=	=	PRON
ejpam-5494	212	24	k∑	k∑	VERB
ejpam-5494	213	1	n=0	n=0	PUNCT
ejpam-5494	213	2	e−x	e−x	PROPN
ejpam-5494	213	3	tnγ	tnγ	PRON
ejpam-5494	213	4	γ(nγ	γ(nγ	NOUN
ejpam-5494	213	5	+	+	CCONJ
ejpam-5494	213	6	1	1	X
ejpam-5494	213	7	)	)	PUNCT
ejpam-5494	213	8	=	=	SYM
ejpam-5494	213	9	e−x	e−x	PROPN
ejpam-5494	213	10	k∑	k∑	PROPN
ejpam-5494	213	11	n=0	n=0	NUM
ejpam-5494	213	12	tnγ	tnγ	NOUN
ejpam-5494	213	13	γ(nγ	γ(nγ	NOUN
ejpam-5494	213	14	+	+	CCONJ
ejpam-5494	213	15	1	1	NUM
ejpam-5494	213	16	)	)	PUNCT
ejpam-5494	213	17	.	.	PUNCT
ejpam-5494	214	1	it	it	PRON
ejpam-5494	214	2	is	be	AUX
ejpam-5494	214	3	important	important	ADJ
ejpam-5494	214	4	to	to	PART
ejpam-5494	214	5	note	note	VERB
ejpam-5494	214	6	that	that	SCONJ
ejpam-5494	214	7	when	when	SCONJ
ejpam-5494	214	8	k	k	PROPN
ejpam-5494	214	9	→	→	SYM
ejpam-5494	214	10	∞	∞	PROPN
ejpam-5494	214	11	,	,	PUNCT
ejpam-5494	214	12	the	the	DET
ejpam-5494	214	13	approximate	approximate	ADJ
ejpam-5494	214	14	solution	solution	NOUN
ejpam-5494	214	15	converges	converge	VERB
ejpam-5494	214	16	on	on	ADP
ejpam-5494	214	17	the	the	DET
ejpam-5494	214	18	exact	exact	ADJ
ejpam-5494	214	19	solution	solution	NOUN
ejpam-5494	214	20	u(x	u(x	NOUN
ejpam-5494	214	21	,	,	PUNCT
ejpam-5494	214	22	t	t	NOUN
ejpam-5494	214	23	)	)	PUNCT
ejpam-5494	214	24	=	=	PUNCT
ejpam-5494	215	1	ex	ex	PRON
ejpam-5494	215	2	∞∑	∞∑	NOUN
ejpam-5494	215	3	n=0	n=0	NUM
ejpam-5494	215	4	(	(	PUNCT
ejpam-5494	215	5	−tγ)n	−tγ)n	NOUN
ejpam-5494	215	6	γ(nγ	γ(nγ	NOUN
ejpam-5494	215	7	+	+	CCONJ
ejpam-5494	215	8	1	1	X
ejpam-5494	215	9	)	)	PUNCT
ejpam-5494	215	10	=	=	SYM
ejpam-5494	216	1	exe(−tγ	exe(−tγ	ADJ
ejpam-5494	216	2	)	)	PUNCT
ejpam-5494	216	3	,	,	PUNCT
ejpam-5494	216	4	w(x	w(x	PROPN
ejpam-5494	216	5	,	,	PUNCT
ejpam-5494	216	6	t	t	PROPN
ejpam-5494	216	7	)	)	PUNCT
ejpam-5494	216	8	=	=	SYM
ejpam-5494	216	9	e−x	e−x	PROPN
ejpam-5494	216	10	k∑	k∑	PROPN
ejpam-5494	216	11	n=0	n=0	NUM
ejpam-5494	216	12	tnγ	tnγ	NOUN
ejpam-5494	216	13	γ(nγ	γ(nγ	NOUN
ejpam-5494	216	14	+	+	CCONJ
ejpam-5494	216	15	1	1	X
ejpam-5494	216	16	)	)	PUNCT
ejpam-5494	216	17	=	=	SYM
ejpam-5494	216	18	e−xe(tγ	e−xe(tγ	NOUN
ejpam-5494	216	19	)	)	PUNCT
ejpam-5494	216	20	.	.	PUNCT
ejpam-5494	217	1	if	if	SCONJ
ejpam-5494	217	2	γ	γ	X
ejpam-5494	217	3	=	=	SYM
ejpam-5494	217	4	1	1	NUM
ejpam-5494	217	5	,	,	PUNCT
ejpam-5494	217	6	the	the	DET
ejpam-5494	217	7	solutions	solution	NOUN
ejpam-5494	217	8	is	be	AUX
ejpam-5494	217	9	the	the	DET
ejpam-5494	217	10	exact	exact	ADJ
ejpam-5494	217	11	solution	solution	NOUN
ejpam-5494	217	12	of	of	ADP
ejpam-5494	217	13	first	first	ADJ
ejpam-5494	217	14	-	-	PUNCT
ejpam-5494	217	15	order	order	NOUN
ejpam-5494	217	16	nonlinear	nonlinear	ADJ
ejpam-5494	217	17	pdes	pde	NOUN
ejpam-5494	217	18	system	system	NOUN
ejpam-5494	217	19	u(x	u(x	NOUN
ejpam-5494	217	20	,	,	PUNCT
ejpam-5494	217	21	t	t	NOUN
ejpam-5494	217	22	)	)	PUNCT
ejpam-5494	218	1	=	=	SYM
ejpam-5494	218	2	ex−t	ex−t	NOUN
ejpam-5494	218	3	,	,	PUNCT
ejpam-5494	218	4	w(x	w(x	PROPN
ejpam-5494	218	5	,	,	PUNCT
ejpam-5494	218	6	t	t	PROPN
ejpam-5494	218	7	)	)	PUNCT
ejpam-5494	218	8	=	=	PUNCT
ejpam-5494	218	9	e−x+t	e−x+t	NOUN
ejpam-5494	218	10	.	.	PUNCT
ejpam-5494	219	1	the	the	DET
ejpam-5494	219	2	approximate	approximate	ADJ
ejpam-5494	219	3	solution	solution	NOUN
ejpam-5494	219	4	for	for	ADP
ejpam-5494	219	5	example	example	NOUN
ejpam-5494	219	6	1	1	NUM
ejpam-5494	219	7	are	be	AUX
ejpam-5494	219	8	shown	show	VERB
ejpam-5494	219	9	in	in	ADP
ejpam-5494	219	10	figure	figure	NOUN
ejpam-5494	219	11	1	1	NUM
ejpam-5494	219	12	.	.	PUNCT
ejpam-5494	219	13	figures	figure	NOUN
ejpam-5494	219	14	2	2	NUM
ejpam-5494	219	15	and	and	CCONJ
ejpam-5494	219	16	3	3	NUM
ejpam-5494	219	17	compare	compare	VERB
ejpam-5494	219	18	the	the	DET
ejpam-5494	219	19	visualizations	visualization	NOUN
ejpam-5494	219	20	to	to	ADP
ejpam-5494	219	21	the	the	DET
ejpam-5494	219	22	approximate	approximate	ADJ
ejpam-5494	219	23	and	and	CCONJ
ejpam-5494	219	24	exact	exact	ADJ
ejpam-5494	219	25	solutions	solution	NOUN
ejpam-5494	219	26	.	.	PUNCT
ejpam-5494	220	1	figure	figure	VERB
ejpam-5494	220	2	4	4	NUM
ejpam-5494	220	3	:	:	PUNCT
ejpam-5494	220	4	subplot	subplot	NOUN
ejpam-5494	220	5	(	(	PUNCT
ejpam-5494	220	6	a	a	X
ejpam-5494	220	7	)	)	PUNCT
ejpam-5494	220	8	depicts	depict	VERB
ejpam-5494	220	9	the	the	DET
ejpam-5494	220	10	approximate	approximate	ADJ
ejpam-5494	220	11	solution	solution	NOUN
ejpam-5494	220	12	u5(x	u5(x	PROPN
ejpam-5494	220	13	,	,	PUNCT
ejpam-5494	220	14	y	y	PROPN
ejpam-5494	220	15	,	,	PUNCT
ejpam-5494	220	16	t	t	PROPN
ejpam-5494	220	17	)	)	PUNCT
ejpam-5494	220	18	and	and	CCONJ
ejpam-5494	220	19	subplot	subplot	NOUN
ejpam-5494	220	20	(	(	PUNCT
ejpam-5494	220	21	b	b	NOUN
ejpam-5494	220	22	)	)	PUNCT
ejpam-5494	220	23	presents	present	VERB
ejpam-5494	220	24	the	the	DET
ejpam-5494	220	25	approximate	approximate	ADJ
ejpam-5494	220	26	solution	solution	NOUN
ejpam-5494	220	27	w5(x	w5(x	PROPN
ejpam-5494	220	28	,	,	PUNCT
ejpam-5494	220	29	y	y	PROPN
ejpam-5494	220	30	,	,	PUNCT
ejpam-5494	220	31	t	t	PROPN
ejpam-5494	220	32	)	)	PUNCT
ejpam-5494	220	33	for	for	ADP
ejpam-5494	220	34	example	example	NOUN
ejpam-5494	220	35	2	2	NUM
ejpam-5494	220	36	at	at	ADP
ejpam-5494	220	37	different	different	ADJ
ejpam-5494	220	38	γ	γ	NOUN
ejpam-5494	220	39	values	value	NOUN
ejpam-5494	220	40	for	for	ADP
ejpam-5494	220	41	x	x	SYM
ejpam-5494	220	42	=	=	PUNCT
ejpam-5494	220	43	y	y	PROPN
ejpam-5494	220	44	=	=	SYM
ejpam-5494	220	45	0.2	0.2	NUM
ejpam-5494	220	46	.	.	PUNCT
ejpam-5494	220	47	example	example	NOUN
ejpam-5494	221	1	2	2	NUM
ejpam-5494	221	2	.	.	PUNCT
ejpam-5494	222	1	[	[	X
ejpam-5494	222	2	6	6	NUM
ejpam-5494	222	3	]	]	PUNCT
ejpam-5494	222	4	consider	consider	VERB
ejpam-5494	222	5	the	the	DET
ejpam-5494	222	6	fractional	fractional	ADJ
ejpam-5494	222	7	reaction	reaction	NOUN
ejpam-5494	222	8	-	-	PUNCT
ejpam-5494	222	9	diffusion	diffusion	NOUN
ejpam-5494	222	10	brusselator	brusselator	NOUN
ejpam-5494	222	11	system	system	NOUN
ejpam-5494	222	12	dγ	dγ	PROPN
ejpam-5494	222	13	t	t	PROPN
ejpam-5494	222	14	u(x	u(x	PROPN
ejpam-5494	222	15	,	,	PUNCT
ejpam-5494	222	16	y	y	PROPN
ejpam-5494	222	17	,	,	PUNCT
ejpam-5494	222	18	t	t	PROPN
ejpam-5494	222	19	)	)	PUNCT
ejpam-5494	222	20	=	=	SYM
ejpam-5494	222	21	−2u(x	−2u(x	PROPN
ejpam-5494	222	22	,	,	PUNCT
ejpam-5494	222	23	y	y	PROPN
ejpam-5494	222	24	,	,	PUNCT
ejpam-5494	222	25	t	t	PROPN
ejpam-5494	222	26	)	)	PUNCT
ejpam-5494	223	1	+	+	CCONJ
ejpam-5494	223	2	u2(x	u2(x	PROPN
ejpam-5494	223	3	,	,	PUNCT
ejpam-5494	223	4	y	y	NOUN
ejpam-5494	223	5	,	,	PUNCT
ejpam-5494	223	6	t)w(x	t)w(x	NOUN
ejpam-5494	223	7	,	,	PUNCT
ejpam-5494	223	8	y	y	PROPN
ejpam-5494	223	9	,	,	PUNCT
ejpam-5494	223	10	t	t	PROPN
ejpam-5494	223	11	)	)	PUNCT
ejpam-5494	223	12	+	+	CCONJ
ejpam-5494	223	13	1	1	NUM
ejpam-5494	223	14	4	4	NUM
ejpam-5494	223	15	[	[	PUNCT
ejpam-5494	223	16	uxx(x	uxx(x	PROPN
ejpam-5494	223	17	,	,	PUNCT
ejpam-5494	223	18	y	y	PROPN
ejpam-5494	223	19	,	,	PUNCT
ejpam-5494	223	20	t	t	PROPN
ejpam-5494	223	21	)	)	PUNCT
ejpam-5494	223	22	+	+	CCONJ
ejpam-5494	223	23	uyy(x	uyy(x	PROPN
ejpam-5494	223	24	,	,	PUNCT
ejpam-5494	223	25	y	y	PROPN
ejpam-5494	223	26	,	,	PUNCT
ejpam-5494	223	27	t	t	PROPN
ejpam-5494	223	28	)	)	PUNCT
ejpam-5494	223	29	]	]	PUNCT
ejpam-5494	223	30	,	,	PUNCT
ejpam-5494	223	31	dγ	dγ	PROPN
ejpam-5494	223	32	t	t	PROPN
ejpam-5494	223	33	w(x	w(x	PROPN
ejpam-5494	223	34	,	,	PUNCT
ejpam-5494	223	35	y	y	PROPN
ejpam-5494	223	36	,	,	PUNCT
ejpam-5494	223	37	t	t	PROPN
ejpam-5494	223	38	)	)	PUNCT
ejpam-5494	223	39	=	=	SYM
ejpam-5494	223	40	u(x	u(x	PROPN
ejpam-5494	223	41	,	,	PUNCT
ejpam-5494	223	42	y	y	NOUN
ejpam-5494	223	43	,	,	PUNCT
ejpam-5494	223	44	t)−	t)−	PROPN
ejpam-5494	223	45	u2(x	u2(x	PROPN
ejpam-5494	223	46	,	,	PUNCT
ejpam-5494	223	47	y	y	PROPN
ejpam-5494	223	48	,	,	PUNCT
ejpam-5494	223	49	t)w(x	t)w(x	NOUN
ejpam-5494	223	50	,	,	PUNCT
ejpam-5494	223	51	y	y	PROPN
ejpam-5494	223	52	,	,	PUNCT
ejpam-5494	223	53	t	t	PROPN
ejpam-5494	223	54	)	)	PUNCT
ejpam-5494	223	55	+	+	CCONJ
ejpam-5494	223	56	1	1	NUM
ejpam-5494	223	57	4	4	NUM
ejpam-5494	223	58	[	[	X
ejpam-5494	223	59	wxx(x	wxx(x	PROPN
ejpam-5494	223	60	,	,	PUNCT
ejpam-5494	223	61	y	y	PROPN
ejpam-5494	223	62	,	,	PUNCT
ejpam-5494	223	63	t	t	PROPN
ejpam-5494	223	64	)	)	PUNCT
ejpam-5494	223	65	+	+	CCONJ
ejpam-5494	223	66	wyy(x	wyy(x	PROPN
ejpam-5494	223	67	,	,	PUNCT
ejpam-5494	223	68	y	y	PROPN
ejpam-5494	223	69	,	,	PUNCT
ejpam-5494	223	70	t	t	PROPN
ejpam-5494	223	71	)	)	PUNCT
ejpam-5494	223	72	]	]	PUNCT
ejpam-5494	223	73	,	,	PUNCT
ejpam-5494	223	74	subject	subject	ADJ
ejpam-5494	223	75	to	to	ADP
ejpam-5494	223	76	the	the	DET
ejpam-5494	223	77	initial	initial	ADJ
ejpam-5494	223	78	conditions	condition	NOUN
ejpam-5494	223	79	u(x	u(x	NOUN
ejpam-5494	223	80	,	,	PUNCT
ejpam-5494	223	81	y	y	NOUN
ejpam-5494	223	82	,	,	PUNCT
ejpam-5494	223	83	0	0	NUM
ejpam-5494	223	84	)	)	PUNCT
ejpam-5494	223	85	=	=	SYM
ejpam-5494	223	86	e−x−y	e−x−y	NOUN
ejpam-5494	223	87	,	,	PUNCT
ejpam-5494	223	88	w(x	w(x	PROPN
ejpam-5494	223	89	,	,	PUNCT
ejpam-5494	223	90	y	y	PROPN
ejpam-5494	223	91	,	,	PUNCT
ejpam-5494	223	92	0	0	NUM
ejpam-5494	223	93	)	)	PUNCT
ejpam-5494	223	94	=	=	SYM
ejpam-5494	224	1	ex+y	ex+y	PROPN
ejpam-5494	224	2	.	.	PUNCT
ejpam-5494	225	1	the	the	DET
ejpam-5494	225	2	exact	exact	ADJ
ejpam-5494	225	3	solution	solution	NOUN
ejpam-5494	225	4	when	when	SCONJ
ejpam-5494	225	5	γ	γ	X
ejpam-5494	225	6	=	=	SYM
ejpam-5494	225	7	1	1	NUM
ejpam-5494	225	8	is	be	AUX
ejpam-5494	225	9	u(x	u(x	NOUN
ejpam-5494	225	10	,	,	PUNCT
ejpam-5494	225	11	y	y	PROPN
ejpam-5494	225	12	,	,	PUNCT
ejpam-5494	225	13	t	t	PROPN
ejpam-5494	225	14	)	)	PUNCT
ejpam-5494	225	15	=	=	PUNCT
ejpam-5494	226	1	e−x−y−	e−x−y−	PROPN
ejpam-5494	226	2	1	1	NUM
ejpam-5494	226	3	2	2	NUM
ejpam-5494	226	4	t	t	PROPN
ejpam-5494	226	5	,	,	PUNCT
ejpam-5494	226	6	w(x	w(x	PROPN
ejpam-5494	226	7	,	,	PUNCT
ejpam-5494	226	8	y	y	PROPN
ejpam-5494	226	9	,	,	PUNCT
ejpam-5494	226	10	t	t	PROPN
ejpam-5494	226	11	)	)	PUNCT
ejpam-5494	226	12	=	=	VERB
ejpam-5494	227	1	ex+y+	ex+y+	VERB
ejpam-5494	227	2	1	1	NUM
ejpam-5494	227	3	2	2	NUM
ejpam-5494	227	4	t.	t.	NOUN
ejpam-5494	227	5	p.	p.	NOUN
ejpam-5494	227	6	pue	pue	NOUN
ejpam-5494	227	7	-	-	PUNCT
ejpam-5494	227	8	on	on	ADP
ejpam-5494	227	9	/	/	SYM
ejpam-5494	227	10	eur	eur	NOUN
ejpam-5494	227	11	.	.	PUNCT
ejpam-5494	228	1	j.	j.	PROPN
ejpam-5494	228	2	pure	pure	PROPN
ejpam-5494	228	3	appl	appl	PROPN
ejpam-5494	228	4	.	.	PROPN
ejpam-5494	228	5	math	math	PROPN
ejpam-5494	228	6	,	,	PUNCT
ejpam-5494	228	7	17	17	NUM
ejpam-5494	228	8	(	(	PUNCT
ejpam-5494	228	9	4	4	NUM
ejpam-5494	228	10	)	)	PUNCT
ejpam-5494	228	11	(	(	PUNCT
ejpam-5494	228	12	2024	2024	NUM
ejpam-5494	228	13	)	)	PUNCT
ejpam-5494	228	14	,	,	PUNCT
ejpam-5494	228	15	3826	3826	NUM
ejpam-5494	228	16	-	-	SYM
ejpam-5494	228	17	3846	3846	NUM
ejpam-5494	228	18	3837	3837	NUM
ejpam-5494	228	19	figure	figure	NOUN
ejpam-5494	228	20	5	5	NUM
ejpam-5494	228	21	:	:	PUNCT
ejpam-5494	228	22	the	the	DET
ejpam-5494	228	23	graphics	graphic	NOUN
ejpam-5494	228	24	represent	represent	VERB
ejpam-5494	228	25	the	the	DET
ejpam-5494	228	26	approximate	approximate	ADJ
ejpam-5494	228	27	solution	solution	NOUN
ejpam-5494	228	28	u5(x	u5(x	PROPN
ejpam-5494	228	29	,	,	PUNCT
ejpam-5494	228	30	y	y	PROPN
ejpam-5494	228	31	,	,	PUNCT
ejpam-5494	228	32	t	t	PROPN
ejpam-5494	228	33	)	)	PUNCT
ejpam-5494	228	34	when	when	SCONJ
ejpam-5494	228	35	t	t	NOUN
ejpam-5494	228	36	=	=	SYM
ejpam-5494	228	37	1	1	NUM
ejpam-5494	228	38	,	,	PUNCT
ejpam-5494	228	39	0	0	NUM
ejpam-5494	228	40	⩽	⩽	NOUN
ejpam-5494	228	41	x	x	SYM
ejpam-5494	228	42	,	,	PUNCT
ejpam-5494	228	43	y	y	PROPN
ejpam-5494	228	44	⩽	⩽	PROPN
ejpam-5494	228	45	1	1	NUM
ejpam-5494	228	46	,	,	PUNCT
ejpam-5494	228	47	with	with	ADP
ejpam-5494	228	48	different	different	ADJ
ejpam-5494	228	49	γ	γ	NOUN
ejpam-5494	228	50	values	value	NOUN
ejpam-5494	228	51	:	:	PUNCT
ejpam-5494	228	52	(	(	PUNCT
ejpam-5494	228	53	a	a	X
ejpam-5494	228	54	)	)	PUNCT
ejpam-5494	228	55	γ	γ	NOUN
ejpam-5494	228	56	=	=	SYM
ejpam-5494	228	57	0.6	0.6	NUM
ejpam-5494	228	58	,	,	PUNCT
ejpam-5494	228	59	(	(	PUNCT
ejpam-5494	228	60	b	b	X
ejpam-5494	228	61	)	)	PUNCT
ejpam-5494	228	62	γ	γ	NOUN
ejpam-5494	228	63	=	=	NUM
ejpam-5494	228	64	0.8	0.8	NUM
ejpam-5494	228	65	,	,	PUNCT
ejpam-5494	228	66	(	(	PUNCT
ejpam-5494	228	67	c	c	X
ejpam-5494	228	68	)	)	PUNCT
ejpam-5494	228	69	γ	γ	NOUN
ejpam-5494	228	70	=	=	SYM
ejpam-5494	228	71	1	1	NUM
ejpam-5494	228	72	,	,	PUNCT
ejpam-5494	228	73	and	and	CCONJ
ejpam-5494	228	74	(	(	PUNCT
ejpam-5494	228	75	d	d	X
ejpam-5494	228	76	)	)	PUNCT
ejpam-5494	228	77	the	the	DET
ejpam-5494	228	78	exact	exact	ADJ
ejpam-5494	228	79	solution	solution	NOUN
ejpam-5494	228	80	for	for	ADP
ejpam-5494	228	81	example	example	NOUN
ejpam-5494	228	82	2	2	NUM
ejpam-5494	228	83	.	.	X
ejpam-5494	228	84	note	note	VERB
ejpam-5494	228	85	that	that	SCONJ
ejpam-5494	228	86	n1(u	n1(u	X
ejpam-5494	228	87	,	,	PUNCT
ejpam-5494	228	88	w	w	NOUN
ejpam-5494	228	89	)	)	PUNCT
ejpam-5494	228	90	=	=	SYM
ejpam-5494	229	1	−2u	−2u	PROPN
ejpam-5494	229	2	+	+	CCONJ
ejpam-5494	229	3	u2w	u2w	ADJ
ejpam-5494	229	4	+	+	CCONJ
ejpam-5494	229	5	1	1	NUM
ejpam-5494	229	6	4(uxx	4(uxx	NOUN
ejpam-5494	229	7	+	+	CCONJ
ejpam-5494	229	8	uyy	uyy	PROPN
ejpam-5494	229	9	)	)	PUNCT
ejpam-5494	229	10	,	,	PUNCT
ejpam-5494	229	11	n2(u	n2(u	PROPN
ejpam-5494	229	12	,	,	PUNCT
ejpam-5494	229	13	w	w	NOUN
ejpam-5494	229	14	)	)	PUNCT
ejpam-5494	229	15	=	=	SYM
ejpam-5494	229	16	u	u	NOUN
ejpam-5494	229	17	−	−	NOUN
ejpam-5494	229	18	u2w2	u2w2	NOUN
ejpam-5494	229	19	x	x	X
ejpam-5494	229	20	+	+	PUNCT
ejpam-5494	229	21	1	1	NUM
ejpam-5494	229	22	4(wxx	4(wxx	NUM
ejpam-5494	229	23	+	+	CCONJ
ejpam-5494	229	24	wyy	wyy	NOUN
ejpam-5494	229	25	)	)	PUNCT
ejpam-5494	229	26	,	,	PUNCT
ejpam-5494	229	27	f1(x	f1(x	PROPN
ejpam-5494	229	28	,	,	PUNCT
ejpam-5494	229	29	t	t	PROPN
ejpam-5494	229	30	)	)	PUNCT
ejpam-5494	229	31	=	=	SYM
ejpam-5494	230	1	f2(x	f2(x	PROPN
ejpam-5494	230	2	,	,	PUNCT
ejpam-5494	230	3	t	t	PROPN
ejpam-5494	230	4	)	)	PUNCT
ejpam-5494	230	5	=	=	SYM
ejpam-5494	230	6	0	0	NUM
ejpam-5494	230	7	,	,	PUNCT
ejpam-5494	230	8	g1(x	g1(x	NOUN
ejpam-5494	230	9	,	,	PUNCT
ejpam-5494	230	10	y	y	NOUN
ejpam-5494	230	11	)	)	PUNCT
ejpam-5494	230	12	=	=	SYM
ejpam-5494	230	13	e−x−y	e−x−y	NOUN
ejpam-5494	230	14	,	,	PUNCT
ejpam-5494	230	15	g2(x	g2(x	PROPN
ejpam-5494	230	16	,	,	PUNCT
ejpam-5494	230	17	y	y	PROPN
ejpam-5494	230	18	)	)	PUNCT
ejpam-5494	230	19	=	=	SYM
ejpam-5494	231	1	ex+y	ex+y	PROPN
ejpam-5494	231	2	.	.	PUNCT
ejpam-5494	232	1	the	the	DET
ejpam-5494	232	2	kth−	kth−	PROPN
ejpam-5494	232	3	truncated	truncated	ADJ
ejpam-5494	232	4	term	term	NOUN
ejpam-5494	232	5	series	series	NOUN
ejpam-5494	232	6	solution	solution	NOUN
ejpam-5494	232	7	to	to	ADP
ejpam-5494	232	8	the	the	DET
ejpam-5494	232	9	problem	problem	NOUN
ejpam-5494	232	10	is	be	AUX
ejpam-5494	232	11	uk(x	uk(x	ADV
ejpam-5494	232	12	,	,	PUNCT
ejpam-5494	232	13	y	y	PROPN
ejpam-5494	232	14	,	,	PUNCT
ejpam-5494	232	15	t	t	PROPN
ejpam-5494	232	16	)	)	PUNCT
ejpam-5494	232	17	=	=	PUNCT
ejpam-5494	232	18	k∑	k∑	PROPN
ejpam-5494	232	19	n=0	n=0	NUM
ejpam-5494	232	20	an(x	an(x	ADP
ejpam-5494	232	21	,	,	PUNCT
ejpam-5494	232	22	y	y	NOUN
ejpam-5494	232	23	)	)	PUNCT
ejpam-5494	232	24	tnγ	tnγ	NOUN
ejpam-5494	232	25	γ(nγ	γ(nγ	NOUN
ejpam-5494	232	26	+	+	CCONJ
ejpam-5494	232	27	1	1	X
ejpam-5494	232	28	)	)	PUNCT
ejpam-5494	232	29	and	and	CCONJ
ejpam-5494	232	30	wk(x	wk(x	NOUN
ejpam-5494	232	31	,	,	PUNCT
ejpam-5494	232	32	y	y	PROPN
ejpam-5494	232	33	,	,	PUNCT
ejpam-5494	232	34	t	t	PROPN
ejpam-5494	232	35	)	)	PUNCT
ejpam-5494	232	36	=	=	PUNCT
ejpam-5494	232	37	k∑	k∑	PROPN
ejpam-5494	232	38	n=0	n=0	PUNCT
ejpam-5494	232	39	bn(x	bn(x	NUM
ejpam-5494	232	40	,	,	PUNCT
ejpam-5494	232	41	y	y	NOUN
ejpam-5494	232	42	)	)	PUNCT
ejpam-5494	232	43	tnγ	tnγ	NOUN
ejpam-5494	232	44	γ(nγ	γ(nγ	NOUN
ejpam-5494	232	45	+	+	CCONJ
ejpam-5494	232	46	1	1	NUM
ejpam-5494	232	47	)	)	PUNCT
ejpam-5494	232	48	.	.	PUNCT
ejpam-5494	233	1	the	the	DET
ejpam-5494	233	2	recursive	recursive	ADJ
ejpam-5494	233	3	relation	relation	NOUN
ejpam-5494	233	4	for	for	ADP
ejpam-5494	233	5	this	this	DET
ejpam-5494	233	6	problem	problem	NOUN
ejpam-5494	233	7	is	be	AUX
ejpam-5494	233	8	u0(x	u0(x	PROPN
ejpam-5494	233	9	,	,	PUNCT
ejpam-5494	233	10	y	y	PROPN
ejpam-5494	233	11	,	,	PUNCT
ejpam-5494	233	12	t	t	PROPN
ejpam-5494	233	13	)	)	PUNCT
ejpam-5494	233	14	=	=	SYM
ejpam-5494	233	15	e−x−y	e−x−y	NOUN
ejpam-5494	233	16	,	,	PUNCT
ejpam-5494	233	17	w0(x	w0(x	PROPN
ejpam-5494	233	18	,	,	PUNCT
ejpam-5494	233	19	y	y	PROPN
ejpam-5494	233	20	,	,	PUNCT
ejpam-5494	233	21	t	t	PROPN
ejpam-5494	233	22	)	)	PUNCT
ejpam-5494	234	1	=	=	SYM
ejpam-5494	234	2	ex+y	ex+y	PROPN
ejpam-5494	234	3	,	,	PUNCT
ejpam-5494	234	4	res1,k(x	res1,k(x	NOUN
ejpam-5494	234	5	,	,	PUNCT
ejpam-5494	234	6	y	y	PROPN
ejpam-5494	234	7	,	,	PUNCT
ejpam-5494	234	8	t	t	PROPN
ejpam-5494	234	9	)	)	PUNCT
ejpam-5494	234	10	=	=	PUNCT
ejpam-5494	235	1	uk(x	uk(x	PROPN
ejpam-5494	235	2	,	,	PUNCT
ejpam-5494	235	3	y	y	PROPN
ejpam-5494	235	4	,	,	PUNCT
ejpam-5494	235	5	t)−	t)−	PROPN
ejpam-5494	235	6	e−x−y	e−x−y	NOUN
ejpam-5494	235	7	+	+	CCONJ
ejpam-5494	235	8	2s−1	2s−1	NUM
ejpam-5494	235	9	[	[	PUNCT
ejpam-5494	235	10	1	1	NUM
ejpam-5494	235	11	vγα	vγα	NOUN
ejpam-5494	235	12	s	s	X
ejpam-5494	235	13	[	[	PUNCT
ejpam-5494	235	14	uk−1	uk−1	PROPN
ejpam-5494	235	15	]	]	X
ejpam-5494	235	16	]	]	X
ejpam-5494	235	17	−	−	PROPN
ejpam-5494	236	1	s−1	s−1	PROPN
ejpam-5494	236	2	[	[	PUNCT
ejpam-5494	236	3	1	1	NUM
ejpam-5494	236	4	vγα	vγα	PROPN
ejpam-5494	236	5	s	s	X
ejpam-5494	236	6	[	[	PUNCT
ejpam-5494	236	7	u2k−1wk−1	u2k−1wk−1	PROPN
ejpam-5494	236	8	]	]	X
ejpam-5494	236	9	]	]	X
ejpam-5494	236	10	−	−	PROPN
ejpam-5494	236	11	1	1	NUM
ejpam-5494	236	12	4	4	NUM
ejpam-5494	236	13	s−1	s−1	PROPN
ejpam-5494	236	14	[	[	PUNCT
ejpam-5494	236	15	1	1	NUM
ejpam-5494	236	16	vγα	vγα	NOUN
ejpam-5494	236	17	s	s	X
ejpam-5494	236	18	[	[	PUNCT
ejpam-5494	236	19	(	(	PUNCT
ejpam-5494	236	20	uk−1)xx	uk−1)xx	ADP
ejpam-5494	236	21	+	+	CCONJ
ejpam-5494	236	22	(	(	PUNCT
ejpam-5494	236	23	uk−1)yy	uk−1)yy	PROPN
ejpam-5494	236	24	]	]	X
ejpam-5494	236	25	]	]	PUNCT
ejpam-5494	236	26	,	,	PUNCT
ejpam-5494	236	27	k	k	PROPN
ejpam-5494	236	28	⩾	⩾	PROPN
ejpam-5494	236	29	1	1	NUM
ejpam-5494	236	30	res2,k(x	res2,k(x	VERB
ejpam-5494	236	31	,	,	PUNCT
ejpam-5494	236	32	y	y	PROPN
ejpam-5494	236	33	,	,	PUNCT
ejpam-5494	236	34	t	t	PROPN
ejpam-5494	236	35	)	)	PUNCT
ejpam-5494	236	36	=	=	SYM
ejpam-5494	237	1	wk(x	wk(x	PROPN
ejpam-5494	237	2	,	,	PUNCT
ejpam-5494	237	3	y	y	PROPN
ejpam-5494	237	4	,	,	PUNCT
ejpam-5494	237	5	t)−	t)−	PROPN
ejpam-5494	237	6	ex+y	ex+y	NOUN
ejpam-5494	238	1	−	−	PUNCT
ejpam-5494	238	2	s−1	s−1	PROPN
ejpam-5494	238	3	[	[	PUNCT
ejpam-5494	238	4	1	1	NUM
ejpam-5494	238	5	vγα	vγα	NOUN
ejpam-5494	238	6	s	s	X
ejpam-5494	238	7	[	[	PUNCT
ejpam-5494	238	8	uk−1	uk−1	PROPN
ejpam-5494	238	9	]	]	X
ejpam-5494	238	10	]	]	X
ejpam-5494	239	1	+	+	CCONJ
ejpam-5494	239	2	s−1	s−1	PROPN
ejpam-5494	239	3	[	[	PUNCT
ejpam-5494	239	4	1	1	NUM
ejpam-5494	239	5	vγα	vγα	NOUN
ejpam-5494	239	6	s	s	X
ejpam-5494	239	7	[	[	PUNCT
ejpam-5494	239	8	(	(	PUNCT
ejpam-5494	239	9	uk−1	uk−1	NOUN
ejpam-5494	239	10	)	)	PUNCT
ejpam-5494	239	11	2wk−1	2wk−1	NUM
ejpam-5494	239	12	]	]	PUNCT
ejpam-5494	239	13	]	]	X
ejpam-5494	239	14	−	−	PROPN
ejpam-5494	239	15	1	1	NUM
ejpam-5494	239	16	4	4	NUM
ejpam-5494	239	17	s−1	s−1	PROPN
ejpam-5494	239	18	[	[	PUNCT
ejpam-5494	239	19	1	1	NUM
ejpam-5494	239	20	vγα	vγα	NOUN
ejpam-5494	239	21	s	s	X
ejpam-5494	239	22	[	[	PUNCT
ejpam-5494	239	23	(	(	PUNCT
ejpam-5494	239	24	wk−1)xx	wk−1)xx	ADP
ejpam-5494	239	25	+	+	CCONJ
ejpam-5494	239	26	(	(	PUNCT
ejpam-5494	239	27	wk−1)yy	wk−1)yy	PROPN
ejpam-5494	239	28	]	]	X
ejpam-5494	239	29	]	]	PUNCT
ejpam-5494	239	30	,	,	PUNCT
ejpam-5494	239	31	k	k	PROPN
ejpam-5494	239	32	⩾	⩾	NOUN
ejpam-5494	239	33	1	1	X
ejpam-5494	239	34	.	.	X
ejpam-5494	239	35	proceed	proceed	VERB
ejpam-5494	239	36	to	to	PART
ejpam-5494	239	37	continue	continue	VERB
ejpam-5494	239	38	the	the	DET
ejpam-5494	239	39	recurrence	recurrence	NOUN
ejpam-5494	239	40	to	to	PART
ejpam-5494	239	41	obtain	obtain	VERB
ejpam-5494	239	42	the	the	DET
ejpam-5494	239	43	coefficients	coefficient	NOUN
ejpam-5494	239	44	,	,	PUNCT
ejpam-5494	239	45	a1(x	a1(x	NOUN
ejpam-5494	239	46	,	,	PUNCT
ejpam-5494	239	47	y	y	NOUN
ejpam-5494	239	48	)	)	PUNCT
ejpam-5494	239	49	=	=	SYM
ejpam-5494	239	50	−1	−1	NOUN
ejpam-5494	239	51	2	2	NUM
ejpam-5494	239	52	e−x−y	e−x−y	NOUN
ejpam-5494	239	53	,	,	PUNCT
ejpam-5494	239	54	a2(x	a2(x	PROPN
ejpam-5494	239	55	,	,	PUNCT
ejpam-5494	239	56	y	y	NOUN
ejpam-5494	239	57	)	)	PUNCT
ejpam-5494	239	58	=	=	SYM
ejpam-5494	239	59	1	1	NUM
ejpam-5494	239	60	4	4	NUM
ejpam-5494	239	61	e−x−y	e−x−y	NOUN
ejpam-5494	239	62	,	,	PUNCT
ejpam-5494	239	63	.	.	PUNCT
ejpam-5494	239	64	.	.	PUNCT
ejpam-5494	240	1	.	.	PUNCT
ejpam-5494	241	1	,	,	PUNCT
ejpam-5494	241	2	ak(x	ak(x	NUM
ejpam-5494	241	3	,	,	PUNCT
ejpam-5494	241	4	y	y	NOUN
ejpam-5494	241	5	)	)	PUNCT
ejpam-5494	241	6	=	=	SYM
ejpam-5494	241	7	1	1	NUM
ejpam-5494	241	8	(	(	PUNCT
ejpam-5494	241	9	−2)k	−2)k	DET
ejpam-5494	241	10	e−x−y	e−x−y	PROPN
ejpam-5494	241	11	p.	p.	NOUN
ejpam-5494	241	12	pue	pue	PROPN
ejpam-5494	241	13	-	-	PUNCT
ejpam-5494	241	14	on	on	ADP
ejpam-5494	241	15	/	/	SYM
ejpam-5494	241	16	eur	eur	NOUN
ejpam-5494	241	17	.	.	PUNCT
ejpam-5494	242	1	j.	j.	PROPN
ejpam-5494	242	2	pure	pure	PROPN
ejpam-5494	242	3	appl	appl	PROPN
ejpam-5494	242	4	.	.	PROPN
ejpam-5494	242	5	math	math	PROPN
ejpam-5494	242	6	,	,	PUNCT
ejpam-5494	242	7	17	17	NUM
ejpam-5494	242	8	(	(	PUNCT
ejpam-5494	242	9	4	4	NUM
ejpam-5494	242	10	)	)	PUNCT
ejpam-5494	242	11	(	(	PUNCT
ejpam-5494	242	12	2024	2024	NUM
ejpam-5494	242	13	)	)	PUNCT
ejpam-5494	242	14	,	,	PUNCT
ejpam-5494	242	15	3826	3826	NUM
ejpam-5494	242	16	-	-	SYM
ejpam-5494	242	17	3846	3846	NUM
ejpam-5494	242	18	3838	3838	NUM
ejpam-5494	242	19	figure	figure	NOUN
ejpam-5494	242	20	6	6	NUM
ejpam-5494	242	21	:	:	PUNCT
ejpam-5494	242	22	the	the	DET
ejpam-5494	242	23	graphics	graphic	NOUN
ejpam-5494	242	24	represent	represent	VERB
ejpam-5494	242	25	the	the	DET
ejpam-5494	242	26	approximate	approximate	ADJ
ejpam-5494	242	27	solution	solution	NOUN
ejpam-5494	242	28	w5(x	w5(x	PROPN
ejpam-5494	242	29	,	,	PUNCT
ejpam-5494	242	30	y	y	PROPN
ejpam-5494	242	31	,	,	PUNCT
ejpam-5494	242	32	t	t	PROPN
ejpam-5494	242	33	)	)	PUNCT
ejpam-5494	242	34	when	when	SCONJ
ejpam-5494	242	35	t	t	NOUN
ejpam-5494	242	36	=	=	SYM
ejpam-5494	242	37	1	1	NUM
ejpam-5494	242	38	,	,	PUNCT
ejpam-5494	242	39	0	0	NUM
ejpam-5494	242	40	⩽	⩽	NOUN
ejpam-5494	242	41	x	x	SYM
ejpam-5494	242	42	,	,	PUNCT
ejpam-5494	242	43	y	y	PROPN
ejpam-5494	242	44	⩽	⩽	PROPN
ejpam-5494	242	45	1	1	NUM
ejpam-5494	242	46	,	,	PUNCT
ejpam-5494	242	47	with	with	ADP
ejpam-5494	242	48	different	different	ADJ
ejpam-5494	242	49	γ	γ	NOUN
ejpam-5494	242	50	values	value	NOUN
ejpam-5494	242	51	:	:	PUNCT
ejpam-5494	242	52	(	(	PUNCT
ejpam-5494	242	53	a	a	X
ejpam-5494	242	54	)	)	PUNCT
ejpam-5494	242	55	γ	γ	NOUN
ejpam-5494	242	56	=	=	SYM
ejpam-5494	242	57	0.6	0.6	NUM
ejpam-5494	242	58	,	,	PUNCT
ejpam-5494	242	59	(	(	PUNCT
ejpam-5494	242	60	b	b	X
ejpam-5494	242	61	)	)	PUNCT
ejpam-5494	242	62	γ	γ	NOUN
ejpam-5494	242	63	=	=	NUM
ejpam-5494	242	64	0.8	0.8	NUM
ejpam-5494	242	65	,	,	PUNCT
ejpam-5494	242	66	(	(	PUNCT
ejpam-5494	242	67	c	c	X
ejpam-5494	242	68	)	)	PUNCT
ejpam-5494	242	69	γ	γ	NOUN
ejpam-5494	242	70	=	=	SYM
ejpam-5494	242	71	1	1	NUM
ejpam-5494	242	72	,	,	PUNCT
ejpam-5494	242	73	and	and	CCONJ
ejpam-5494	242	74	(	(	PUNCT
ejpam-5494	242	75	d	d	X
ejpam-5494	242	76	)	)	PUNCT
ejpam-5494	242	77	the	the	DET
ejpam-5494	242	78	exact	exact	ADJ
ejpam-5494	242	79	solution	solution	NOUN
ejpam-5494	242	80	for	for	ADP
ejpam-5494	242	81	example	example	NOUN
ejpam-5494	242	82	2	2	NUM
ejpam-5494	242	83	.	.	PUNCT
ejpam-5494	242	84	b1(x	b1(x	NOUN
ejpam-5494	242	85	,	,	PUNCT
ejpam-5494	242	86	y	y	NOUN
ejpam-5494	242	87	)	)	PUNCT
ejpam-5494	242	88	=	=	SYM
ejpam-5494	242	89	1	1	NUM
ejpam-5494	242	90	2	2	NUM
ejpam-5494	242	91	ex+y	ex+y	PROPN
ejpam-5494	242	92	,	,	PUNCT
ejpam-5494	242	93	b2(x	b2(x	PROPN
ejpam-5494	242	94	,	,	PUNCT
ejpam-5494	242	95	y	y	NOUN
ejpam-5494	242	96	)	)	PUNCT
ejpam-5494	242	97	=	=	SYM
ejpam-5494	243	1	1	1	NUM
ejpam-5494	243	2	4	4	NUM
ejpam-5494	243	3	ex+y	ex+y	NUM
ejpam-5494	243	4	,	,	PUNCT
ejpam-5494	243	5	.	.	PUNCT
ejpam-5494	243	6	.	.	PUNCT
ejpam-5494	243	7	.	.	PUNCT
ejpam-5494	244	1	,	,	PUNCT
ejpam-5494	244	2	bk(x	bk(x	PROPN
ejpam-5494	244	3	,	,	PUNCT
ejpam-5494	244	4	y	y	PROPN
ejpam-5494	244	5	)	)	PUNCT
ejpam-5494	244	6	=	=	SYM
ejpam-5494	245	1	1	1	NUM
ejpam-5494	245	2	2k	2k	NUM
ejpam-5494	245	3	ex+y	ex+y	PROPN
ejpam-5494	245	4	.	.	PROPN
ejpam-5494	245	5	hence	hence	ADV
ejpam-5494	245	6	,	,	PUNCT
ejpam-5494	245	7	the	the	DET
ejpam-5494	245	8	k	k	ADJ
ejpam-5494	245	9	-	-	PUNCT
ejpam-5494	245	10	order	order	NOUN
ejpam-5494	245	11	approximate	approximate	ADJ
ejpam-5494	245	12	series	series	NOUN
ejpam-5494	245	13	solution	solution	NOUN
ejpam-5494	245	14	is	be	AUX
ejpam-5494	245	15	uk(x	uk(x	ADV
ejpam-5494	245	16	,	,	PUNCT
ejpam-5494	245	17	y	y	PROPN
ejpam-5494	245	18	,	,	PUNCT
ejpam-5494	245	19	t	t	PROPN
ejpam-5494	245	20	)	)	PUNCT
ejpam-5494	245	21	=	=	SYM
ejpam-5494	246	1	e−x−y	e−x−y	NOUN
ejpam-5494	246	2	[	[	PUNCT
ejpam-5494	246	3	1−	1−	NUM
ejpam-5494	246	4	1	1	NUM
ejpam-5494	246	5	2	2	NUM
ejpam-5494	246	6	tγ	tγ	NOUN
ejpam-5494	246	7	γ(γ	γ(γ	PROPN
ejpam-5494	246	8	+	+	CCONJ
ejpam-5494	246	9	1	1	X
ejpam-5494	246	10	)	)	PUNCT
ejpam-5494	246	11	+	+	CCONJ
ejpam-5494	246	12	1	1	NUM
ejpam-5494	246	13	4	4	NUM
ejpam-5494	246	14	t2γ	t2γ	NOUN
ejpam-5494	246	15	γ(2γ	γ(2γ	NOUN
ejpam-5494	246	16	+	+	NOUN
ejpam-5494	246	17	1	1	X
ejpam-5494	246	18	)	)	PUNCT
ejpam-5494	246	19	+	+	CCONJ
ejpam-5494	246	20	.	.	PUNCT
ejpam-5494	246	21	.	.	PUNCT
ejpam-5494	247	1	.+	.+	NOUN
ejpam-5494	247	2	1	1	NUM
ejpam-5494	247	3	(	(	PUNCT
ejpam-5494	247	4	−2)k	−2)k	X
ejpam-5494	247	5	tkγ	tkγ	X
ejpam-5494	247	6	γ(kγ	γ(kγ	PROPN
ejpam-5494	247	7	+	+	NOUN
ejpam-5494	247	8	1	1	NUM
ejpam-5494	247	9	)	)	PUNCT
ejpam-5494	247	10	]	]	PUNCT
ejpam-5494	247	11	wk(x	wk(x	PROPN
ejpam-5494	247	12	,	,	PUNCT
ejpam-5494	247	13	y	y	PROPN
ejpam-5494	247	14	,	,	PUNCT
ejpam-5494	247	15	t	t	PROPN
ejpam-5494	247	16	)	)	PUNCT
ejpam-5494	247	17	=	=	SYM
ejpam-5494	248	1	ex+y	ex+y	PROPN
ejpam-5494	248	2	[	[	PUNCT
ejpam-5494	248	3	1	1	NUM
ejpam-5494	248	4	+	+	CCONJ
ejpam-5494	248	5	1	1	NUM
ejpam-5494	248	6	2	2	NUM
ejpam-5494	248	7	tγ	tγ	NOUN
ejpam-5494	248	8	γ(γ	γ(γ	PROPN
ejpam-5494	248	9	+	+	CCONJ
ejpam-5494	248	10	1	1	X
ejpam-5494	248	11	)	)	PUNCT
ejpam-5494	248	12	+	+	CCONJ
ejpam-5494	248	13	1	1	NUM
ejpam-5494	248	14	4	4	NUM
ejpam-5494	248	15	t2γ	t2γ	NOUN
ejpam-5494	248	16	γ(2γ	γ(2γ	NOUN
ejpam-5494	248	17	+	+	NOUN
ejpam-5494	248	18	1	1	X
ejpam-5494	248	19	)	)	PUNCT
ejpam-5494	248	20	+	+	CCONJ
ejpam-5494	248	21	.	.	PUNCT
ejpam-5494	248	22	.	.	PUNCT
ejpam-5494	249	1	.+	.+	NOUN
ejpam-5494	249	2	1	1	NUM
ejpam-5494	249	3	2k	2k	NUM
ejpam-5494	249	4	tkγ	tkγ	ADP
ejpam-5494	249	5	γ(kγ	γ(kγ	PROPN
ejpam-5494	249	6	+	+	NOUN
ejpam-5494	249	7	1	1	NUM
ejpam-5494	249	8	)	)	PUNCT
ejpam-5494	249	9	]	]	PUNCT
ejpam-5494	249	10	.	.	PUNCT
ejpam-5494	250	1	when	when	SCONJ
ejpam-5494	250	2	k	k	PROPN
ejpam-5494	250	3	→	→	SYM
ejpam-5494	250	4	∞	∞	PROPN
ejpam-5494	250	5	,	,	PUNCT
ejpam-5494	250	6	the	the	DET
ejpam-5494	250	7	approximate	approximate	ADJ
ejpam-5494	250	8	solution	solution	NOUN
ejpam-5494	250	9	converges	converge	VERB
ejpam-5494	250	10	to	to	ADP
ejpam-5494	250	11	u(x	u(x	NOUN
ejpam-5494	250	12	,	,	PUNCT
ejpam-5494	250	13	y	y	PROPN
ejpam-5494	250	14	,	,	PUNCT
ejpam-5494	250	15	t	t	PROPN
ejpam-5494	250	16	)	)	PUNCT
ejpam-5494	250	17	=	=	SYM
ejpam-5494	250	18	e−x−y	e−x−y	NOUN
ejpam-5494	250	19	∞∑	∞∑	PROPN
ejpam-5494	250	20	n=0	n=0	PUNCT
ejpam-5494	250	21	(	(	PUNCT
ejpam-5494	250	22	−	−	PROPN
ejpam-5494	250	23	tγ	tγ	NOUN
ejpam-5494	250	24	2	2	NUM
ejpam-5494	250	25	)	)	PUNCT
ejpam-5494	250	26	n	n	CCONJ
ejpam-5494	250	27	γ(nγ	γ(nγ	NOUN
ejpam-5494	250	28	+	+	CCONJ
ejpam-5494	250	29	1	1	X
ejpam-5494	250	30	)	)	PUNCT
ejpam-5494	250	31	=	=	SYM
ejpam-5494	250	32	e−x−ye	e−x−ye	NOUN
ejpam-5494	250	33	(	(	PUNCT
ejpam-5494	250	34	−tγ	−tγ	PROPN
ejpam-5494	250	35	2	2	NUM
ejpam-5494	250	36	)	)	PUNCT
ejpam-5494	250	37	w(x	w(x	PROPN
ejpam-5494	250	38	,	,	PUNCT
ejpam-5494	250	39	y	y	PROPN
ejpam-5494	250	40	,	,	PUNCT
ejpam-5494	250	41	t	t	PROPN
ejpam-5494	250	42	)	)	PUNCT
ejpam-5494	250	43	=	=	SYM
ejpam-5494	251	1	ex+y	ex+y	PROPN
ejpam-5494	251	2	∞∑	∞∑	NOUN
ejpam-5494	251	3	n=0	n=0	NUM
ejpam-5494	251	4	(	(	PUNCT
ejpam-5494	251	5	t	t	PROPN
ejpam-5494	251	6	γ	γ	X
ejpam-5494	251	7	2	2	NUM
ejpam-5494	251	8	)	)	PUNCT
ejpam-5494	251	9	n	n	CCONJ
ejpam-5494	251	10	γ(nγ	γ(nγ	NOUN
ejpam-5494	251	11	+	+	CCONJ
ejpam-5494	251	12	1	1	X
ejpam-5494	251	13	)	)	PUNCT
ejpam-5494	251	14	=	=	PUNCT
ejpam-5494	252	1	ex+ye	ex+ye	PROPN
ejpam-5494	252	2	(	(	PUNCT
ejpam-5494	252	3	tγ	tγ	NOUN
ejpam-5494	252	4	2	2	NUM
ejpam-5494	252	5	)	)	PUNCT
ejpam-5494	252	6	.	.	PUNCT
ejpam-5494	253	1	if	if	SCONJ
ejpam-5494	253	2	γ	γ	X
ejpam-5494	253	3	=	=	SYM
ejpam-5494	253	4	1	1	NUM
ejpam-5494	253	5	,	,	PUNCT
ejpam-5494	253	6	the	the	DET
ejpam-5494	253	7	result	result	NOUN
ejpam-5494	253	8	is	be	AUX
ejpam-5494	253	9	reduced	reduce	VERB
ejpam-5494	253	10	to	to	ADP
ejpam-5494	253	11	the	the	DET
ejpam-5494	253	12	solution	solution	NOUN
ejpam-5494	253	13	of	of	ADP
ejpam-5494	253	14	the	the	DET
ejpam-5494	253	15	first	first	ADJ
ejpam-5494	253	16	-	-	PUNCT
ejpam-5494	253	17	order	order	NOUN
ejpam-5494	253	18	equation	equation	NOUN
ejpam-5494	253	19	u(x	u(x	NOUN
ejpam-5494	253	20	,	,	PUNCT
ejpam-5494	253	21	y	y	PROPN
ejpam-5494	253	22	,	,	PUNCT
ejpam-5494	253	23	t	t	PROPN
ejpam-5494	253	24	)	)	PUNCT
ejpam-5494	253	25	=	=	PUNCT
ejpam-5494	253	26	e−x−y−	e−x−y−	PROPN
ejpam-5494	253	27	1	1	NUM
ejpam-5494	253	28	2	2	NUM
ejpam-5494	253	29	t	t	NOUN
ejpam-5494	253	30	and	and	CCONJ
ejpam-5494	253	31	w(x	w(x	PROPN
ejpam-5494	253	32	,	,	PUNCT
ejpam-5494	253	33	y	y	PROPN
ejpam-5494	253	34	,	,	PUNCT
ejpam-5494	253	35	t	t	PROPN
ejpam-5494	253	36	)	)	PUNCT
ejpam-5494	254	1	=	=	VERB
ejpam-5494	254	2	ex+y+	ex+y+	VERB
ejpam-5494	254	3	1	1	NUM
ejpam-5494	254	4	2	2	NUM
ejpam-5494	254	5	t.	t.	NOUN
ejpam-5494	254	6	the	the	DET
ejpam-5494	254	7	approximate	approximate	ADJ
ejpam-5494	254	8	solution	solution	NOUN
ejpam-5494	254	9	for	for	ADP
ejpam-5494	254	10	example	example	NOUN
ejpam-5494	254	11	2	2	NUM
ejpam-5494	254	12	are	be	AUX
ejpam-5494	254	13	shown	show	VERB
ejpam-5494	254	14	in	in	ADP
ejpam-5494	254	15	figure	figure	NOUN
ejpam-5494	254	16	4	4	NUM
ejpam-5494	254	17	.	.	PUNCT
ejpam-5494	254	18	figures	figure	NOUN
ejpam-5494	254	19	5	5	NUM
ejpam-5494	254	20	and	and	CCONJ
ejpam-5494	254	21	6	6	NUM
ejpam-5494	254	22	compare	compare	VERB
ejpam-5494	254	23	the	the	DET
ejpam-5494	254	24	visualizations	visualization	NOUN
ejpam-5494	254	25	to	to	ADP
ejpam-5494	254	26	the	the	DET
ejpam-5494	254	27	approximate	approximate	ADJ
ejpam-5494	254	28	and	and	CCONJ
ejpam-5494	254	29	exact	exact	ADJ
ejpam-5494	254	30	solutions	solution	NOUN
ejpam-5494	254	31	.	.	PUNCT
ejpam-5494	255	1	p.	p.	NOUN
ejpam-5494	255	2	pue	pue	NOUN
ejpam-5494	255	3	-	-	PUNCT
ejpam-5494	255	4	on	on	ADP
ejpam-5494	255	5	/	/	SYM
ejpam-5494	255	6	eur	eur	NOUN
ejpam-5494	255	7	.	.	PUNCT
ejpam-5494	256	1	j.	j.	PROPN
ejpam-5494	256	2	pure	pure	PROPN
ejpam-5494	256	3	appl	appl	PROPN
ejpam-5494	256	4	.	.	PROPN
ejpam-5494	256	5	math	math	PROPN
ejpam-5494	256	6	,	,	PUNCT
ejpam-5494	256	7	17	17	NUM
ejpam-5494	256	8	(	(	PUNCT
ejpam-5494	256	9	4	4	NUM
ejpam-5494	256	10	)	)	PUNCT
ejpam-5494	256	11	(	(	PUNCT
ejpam-5494	256	12	2024	2024	NUM
ejpam-5494	256	13	)	)	PUNCT
ejpam-5494	256	14	,	,	PUNCT
ejpam-5494	256	15	3826	3826	NUM
ejpam-5494	256	16	-	-	SYM
ejpam-5494	256	17	3846	3846	NUM
ejpam-5494	256	18	3839	3839	NUM
ejpam-5494	256	19	table	table	NOUN
ejpam-5494	256	20	3	3	NUM
ejpam-5494	256	21	:	:	PUNCT
ejpam-5494	256	22	comparison	comparison	NOUN
ejpam-5494	256	23	of	of	ADP
ejpam-5494	256	24	the	the	DET
ejpam-5494	256	25	approximate	approximate	ADJ
ejpam-5494	256	26	solution	solution	NOUN
ejpam-5494	256	27	u5(x	u5(x	PROPN
ejpam-5494	256	28	,	,	PUNCT
ejpam-5494	256	29	y	y	PROPN
ejpam-5494	256	30	,	,	PUNCT
ejpam-5494	256	31	t	t	PROPN
ejpam-5494	256	32	)	)	PUNCT
ejpam-5494	256	33	for	for	ADP
ejpam-5494	256	34	x	x	X
ejpam-5494	256	35	=	=	PUNCT
ejpam-5494	256	36	y	y	PROPN
ejpam-5494	256	37	=	=	NUM
ejpam-5494	256	38	0.2	0.2	NUM
ejpam-5494	256	39	in	in	ADP
ejpam-5494	256	40	example	example	NOUN
ejpam-5494	256	41	2	2	NUM
ejpam-5494	256	42	using	use	VERB
ejpam-5494	256	43	different	different	ADJ
ejpam-5494	256	44	γ	γ	NOUN
ejpam-5494	256	45	values	value	NOUN
ejpam-5494	256	46	.	.	PUNCT
ejpam-5494	257	1	t	t	PROPN
ejpam-5494	257	2	γ	γ	X
ejpam-5494	257	3	=	=	PROPN
ejpam-5494	257	4	0.2	0.2	NUM
ejpam-5494	257	5	γ	γ	X
ejpam-5494	257	6	=	=	SYM
ejpam-5494	257	7	0.4	0.4	NUM
ejpam-5494	257	8	γ	γ	X
ejpam-5494	257	9	=	=	SYM
ejpam-5494	257	10	0.6	0.6	NUM
ejpam-5494	257	11	γ	γ	X
ejpam-5494	257	12	=	=	NOUN
ejpam-5494	257	13	0.8	0.8	NUM
ejpam-5494	257	14	γ	γ	X
ejpam-5494	257	15	=	=	SYM
ejpam-5494	257	16	1	1	NUM
ejpam-5494	257	17	exact	exact	NOUN
ejpam-5494	257	18	soln	soln	NOUN
ejpam-5494	257	19	.	.	PUNCT
ejpam-5494	258	1	0.2	0.2	NUM
ejpam-5494	258	2	0.477488627	0.477488627	NUM
ejpam-5494	258	3	0.512326854	0.512326854	NUM
ejpam-5494	258	4	0.547063183	0.547063183	NUM
ejpam-5494	258	5	0.579385607	0.579385607	NUM
ejpam-5494	258	6	0.606530658	0.606530658	NUM
ejpam-5494	258	7	0.606530659	0.606530659	NUM
ejpam-5494	258	8	0.4	0.4	NUM
ejpam-5494	258	9	0.456444828	0.456444828	NUM
ejpam-5494	258	10	0.474696013	0.474696013	NUM
ejpam-5494	258	11	0.496237125	0.496237125	NUM
ejpam-5494	258	12	0.521635809	0.521635809	NUM
ejpam-5494	258	13	0.548811578	0.548811578	NUM
ejpam-5494	258	14	0.548811636	0.548811636	NUM
ejpam-5494	258	15	0.6	0.6	NUM
ejpam-5494	258	16	0.443011054	0.443011054	NUM
ejpam-5494	258	17	0.449925766	0.449925766	NUM
ejpam-5494	258	18	0.460073110	0.460073110	NUM
ejpam-5494	258	19	0.475641940	0.475641940	NUM
ejpam-5494	258	20	0.496584653	0.496584653	NUM
ejpam-5494	258	21	0.496585303	0.496585303	NUM
ejpam-5494	258	22	0.8	0.8	NUM
ejpam-5494	258	23	0.432811651	0.432811651	NUM
ejpam-5494	258	24	0.430960053	0.430960053	NUM
ejpam-5494	258	25	0.431579433	0.431579433	NUM
ejpam-5494	258	26	0.437159809	0.437159809	NUM
ejpam-5494	258	27	0.449325358	0.449325358	NUM
ejpam-5494	258	28	0.449328964	0.449328964	NUM
ejpam-5494	258	29	1.0	1.0	NUM
ejpam-5494	258	30	0.424420175	0.424420175	NUM
ejpam-5494	258	31	0.415283298	0.415283298	NUM
ejpam-5494	258	32	0.407895963	0.407895963	NUM
ejpam-5494	259	1	0.404110210	0.404110210	NUM
ejpam-5494	259	2	0.406556090	0.406556090	NUM
ejpam-5494	259	3	0.406569659	0.406569659	NUM
ejpam-5494	259	4	table	table	NOUN
ejpam-5494	259	5	4	4	NUM
ejpam-5494	259	6	:	:	PUNCT
ejpam-5494	259	7	comparison	comparison	NOUN
ejpam-5494	259	8	of	of	ADP
ejpam-5494	259	9	the	the	DET
ejpam-5494	259	10	approximate	approximate	ADJ
ejpam-5494	259	11	solution	solution	NOUN
ejpam-5494	259	12	w5(x	w5(x	PROPN
ejpam-5494	259	13	,	,	PUNCT
ejpam-5494	259	14	y	y	PROPN
ejpam-5494	259	15	,	,	PUNCT
ejpam-5494	259	16	t)for	t)for	PROPN
ejpam-5494	259	17	x	x	SYM
ejpam-5494	259	18	=	=	PUNCT
ejpam-5494	259	19	y	y	PROPN
ejpam-5494	259	20	=	=	NUM
ejpam-5494	259	21	0.2	0.2	NUM
ejpam-5494	259	22	in	in	ADP
ejpam-5494	259	23	example	example	NOUN
ejpam-5494	259	24	2	2	NUM
ejpam-5494	259	25	using	use	VERB
ejpam-5494	259	26	different	different	ADJ
ejpam-5494	259	27	γ	γ	NOUN
ejpam-5494	259	28	values	value	NOUN
ejpam-5494	259	29	.	.	PUNCT
ejpam-5494	260	1	t	t	PROPN
ejpam-5494	260	2	γ	γ	X
ejpam-5494	260	3	=	=	PROPN
ejpam-5494	260	4	0.2	0.2	NUM
ejpam-5494	260	5	γ	γ	X
ejpam-5494	260	6	=	=	SYM
ejpam-5494	260	7	0.4	0.4	NUM
ejpam-5494	260	8	γ	γ	X
ejpam-5494	260	9	=	=	SYM
ejpam-5494	260	10	0.6	0.6	NUM
ejpam-5494	260	11	γ	γ	X
ejpam-5494	260	12	=	=	NOUN
ejpam-5494	260	13	0.8	0.8	NUM
ejpam-5494	260	14	γ	γ	X
ejpam-5494	260	15	=	=	SYM
ejpam-5494	260	16	1	1	NUM
ejpam-5494	260	17	exact	exact	NOUN
ejpam-5494	260	18	soln	soln	NOUN
ejpam-5494	260	19	.	.	PUNCT
ejpam-5494	261	1	0.2	0.2	NUM
ejpam-5494	261	2	2.417846010	2.417846010	NUM
ejpam-5494	261	3	2.074372749	2.074372749	NUM
ejpam-5494	261	4	1.865586354	1.865586354	NUM
ejpam-5494	261	5	1.734071972	1.734071972	NUM
ejpam-5494	261	6	1.648721268	1.648721268	NUM
ejpam-5494	261	7	1.648721271	1.648721271	NUM
ejpam-5494	261	8	0.4	0.4	NUM
ejpam-5494	261	9	2.646725351	2.646725351	NUM
ejpam-5494	261	10	2.342078614	2.342078614	NUM
ejpam-5494	261	11	2.111643502	2.111643502	NUM
ejpam-5494	261	12	1.944446048	1.944446048	NUM
ejpam-5494	261	13	1.822118665	1.822118665	NUM
ejpam-5494	261	14	1.822118800	1.822118800	NUM
ejpam-5494	261	15	0.6	0.6	NUM
ejpam-5494	261	16	2.816085119	2.816085119	NUM
ejpam-5494	261	17	2.572130993	2.572130993	NUM
ejpam-5494	261	18	2.344840870	2.344840870	NUM
ejpam-5494	261	19	2.160190740	2.160190740	NUM
ejpam-5494	261	20	2.013751129	2.013751129	NUM
ejpam-5494	261	21	2.013752707	2.013752707	NUM
ejpam-5494	261	22	0.8	0.8	NUM
ejpam-5494	261	23	2.956794558	2.956794558	NUM
ejpam-5494	261	24	2.785737340	2.785737340	NUM
ejpam-5494	261	25	2.577721089	2.577721089	NUM
ejpam-5494	261	26	2.387602322	2.387602322	NUM
ejpam-5494	261	27	2.225531932	2.225531932	NUM
ejpam-5494	261	28	2.225540928	2.225540928	NUM
ejpam-5494	261	29	1.0	1.0	NUM
ejpam-5494	261	30	3.079989436	3.079989436	NUM
ejpam-5494	261	31	2.990722585	2.990722585	NUM
ejpam-5494	261	32	2.815404246	2.815404246	NUM
ejpam-5494	261	33	2.630080531	2.630080531	NUM
ejpam-5494	261	34	2.459568271	2.459568271	NUM
ejpam-5494	261	35	2.459603111	2.459603111	NUM
ejpam-5494	261	36	table	table	NOUN
ejpam-5494	261	37	5	5	NUM
ejpam-5494	261	38	:	:	PUNCT
ejpam-5494	261	39	comparison	comparison	NOUN
ejpam-5494	261	40	of	of	ADP
ejpam-5494	261	41	the	the	DET
ejpam-5494	261	42	absolute	absolute	ADJ
ejpam-5494	261	43	error	error	NOUN
ejpam-5494	261	44	for	for	ADP
ejpam-5494	261	45	u2(x	u2(x	PROPN
ejpam-5494	261	46	,	,	PUNCT
ejpam-5494	261	47	y	y	PROPN
ejpam-5494	261	48	,	,	PUNCT
ejpam-5494	261	49	t	t	PROPN
ejpam-5494	261	50	)	)	PUNCT
ejpam-5494	261	51	when	when	SCONJ
ejpam-5494	261	52	x	x	X
ejpam-5494	261	53	=	=	PUNCT
ejpam-5494	261	54	y	y	PROPN
ejpam-5494	261	55	=	=	PUNCT
ejpam-5494	261	56	0.2	0.2	NUM
ejpam-5494	261	57	and	and	CCONJ
ejpam-5494	261	58	x	x	X
ejpam-5494	261	59	=	=	PUNCT
ejpam-5494	261	60	y	y	NOUN
ejpam-5494	261	61	=	=	SYM
ejpam-5494	261	62	0.5	0.5	NUM
ejpam-5494	261	63	in	in	ADP
ejpam-5494	261	64	example	example	NOUN
ejpam-5494	261	65	2	2	NUM
ejpam-5494	261	66	using	use	VERB
ejpam-5494	261	67	different	different	ADJ
ejpam-5494	261	68	t	t	NOUN
ejpam-5494	261	69	values	value	NOUN
ejpam-5494	261	70	.	.	PUNCT
ejpam-5494	262	1	(	(	PUNCT
ejpam-5494	262	2	x	x	X
ejpam-5494	262	3	,	,	PUNCT
ejpam-5494	262	4	y	y	PROPN
ejpam-5494	262	5	)	)	PUNCT
ejpam-5494	262	6	t	t	PROPN
ejpam-5494	262	7	u2(x	u2(x	PROPN
ejpam-5494	262	8	,	,	PUNCT
ejpam-5494	262	9	y	y	PROPN
ejpam-5494	262	10	,	,	PUNCT
ejpam-5494	262	11	t	t	PROPN
ejpam-5494	262	12	)	)	PUNCT
ejpam-5494	262	13	exact	exact	PROPN
ejpam-5494	262	14	soln	soln	NOUN
ejpam-5494	262	15	.	.	PUNCT
ejpam-5494	263	1	abs	ab	NOUN
ejpam-5494	263	2	.	.	PUNCT
ejpam-5494	264	1	error	error	NOUN
ejpam-5494	264	2	(	(	PUNCT
ejpam-5494	264	3	srpsm	srpsm	ADJ
ejpam-5494	264	4	)	)	PUNCT
ejpam-5494	264	5	abs	ab	NOUN
ejpam-5494	264	6	.	.	PUNCT
ejpam-5494	265	1	error	error	NOUN
ejpam-5494	265	2	(	(	PUNCT
ejpam-5494	265	3	crps)[6	crps)[6	X
ejpam-5494	265	4	]	]	PUNCT
ejpam-5494	265	5	0.2	0.2	NUM
ejpam-5494	265	6	0.6066396416	0.6066396416	NUM
ejpam-5494	265	7	0.6065306597	0.6065306597	NUM
ejpam-5494	265	8	1.089819×	1.089819×	NUM
ejpam-5494	265	9	10−4	10−4	NUM
ejpam-5494	265	10	1.0898×	1.0898×	NUM
ejpam-5494	265	11	10−4	10−4	NUM
ejpam-5494	265	12	(	(	PUNCT
ejpam-5494	265	13	0.2	0.2	NUM
ejpam-5494	265	14	,	,	PUNCT
ejpam-5494	265	15	0.2	0.2	NUM
ejpam-5494	265	16	)	)	PUNCT
ejpam-5494	265	17	0.4	0.4	NUM
ejpam-5494	266	1	0.5496624377	0.5496624377	NUM
ejpam-5494	266	2	0.5488116361	0.5488116361	NUM
ejpam-5494	266	3	8.508016×	8.508016×	NUM
ejpam-5494	266	4	10−4	10−4	NUM
ejpam-5494	266	5	8.5080×	8.5080×	NOUN
ejpam-5494	266	6	10−4	10−4	NUM
ejpam-5494	266	7	0.6	0.6	NUM
ejpam-5494	266	8	0.4993884343	0.4993884343	NUM
ejpam-5494	266	9	0.4965853038	0.4965853038	NUM
ejpam-5494	266	10	2.8031305×	2.8031305×	SYM
ejpam-5494	266	11	10−3	10−3	NUM
ejpam-5494	266	12	2.8031×	2.8031×	NUM
ejpam-5494	266	13	10−3	10−3	NUM
ejpam-5494	266	14	0.8	0.8	NUM
ejpam-5494	266	15	0.4558176313	0.4558176313	NUM
ejpam-5494	266	16	0.4493289641	0.4493289641	NUM
ejpam-5494	266	17	6.4886672×	6.4886672×	NUM
ejpam-5494	266	18	10−3	10−3	NUM
ejpam-5494	266	19	6.4886×	6.4886×	NUM
ejpam-5494	266	20	10−3	10−3	NUM
ejpam-5494	266	21	0.2	0.2	NUM
ejpam-5494	266	22	0.3329308943	0.3329308943	NUM
ejpam-5494	266	23	0.3328710837	0.3328710837	NUM
ejpam-5494	266	24	5.98106×	5.98106×	NUM
ejpam-5494	266	25	10−5	10−5	NUM
ejpam-5494	266	26	5.9810×	5.9810×	NOUN
ejpam-5494	266	27	10−5	10−5	NUM
ejpam-5494	266	28	(	(	PUNCT
ejpam-5494	266	29	0.5	0.5	NUM
ejpam-5494	266	30	,	,	PUNCT
ejpam-5494	266	31	0.5	0.5	NUM
ejpam-5494	266	32	)	)	PUNCT
ejpam-5494	266	33	0.4	0.4	NUM
ejpam-5494	266	34	0.3016611418	0.3016611418	NUM
ejpam-5494	266	35	0.3011942119	0.3011942119	NUM
ejpam-5494	266	36	4.669299×	4.669299×	NUM
ejpam-5494	266	37	10−4	10−4	NUM
ejpam-5494	266	38	4.6692×	4.6692×	NUM
ejpam-5494	266	39	10−4	10−4	NUM
ejpam-5494	266	40	0.6	0.6	NUM
ejpam-5494	266	41	0.2740701836	0.2740701836	NUM
ejpam-5494	266	42	0.2725317930	0.2725317930	NUM
ejpam-5494	266	43	1.5383906×	1.5383906×	NUM
ejpam-5494	266	44	10−3	10−3	NUM
ejpam-5494	266	45	1.5383×	1.5383×	NUM
ejpam-5494	266	46	10−3	10−3	NUM
ejpam-5494	266	47	0.8	0.8	NUM
ejpam-5494	266	48	0.2501580200	0.2501580200	NUM
ejpam-5494	266	49	0.2465969639	0.2465969639	NUM
ejpam-5494	266	50	3.5610561×	3.5610561×	NUM
ejpam-5494	266	51	10−3	10−3	NUM
ejpam-5494	266	52	3.5610×	3.5610×	NUM
ejpam-5494	266	53	10−3	10−3	NUM
ejpam-5494	266	54	table	table	NOUN
ejpam-5494	266	55	6	6	NUM
ejpam-5494	266	56	:	:	PUNCT
ejpam-5494	266	57	comparison	comparison	NOUN
ejpam-5494	266	58	of	of	ADP
ejpam-5494	266	59	the	the	DET
ejpam-5494	266	60	absolute	absolute	ADJ
ejpam-5494	266	61	error	error	NOUN
ejpam-5494	266	62	for	for	ADP
ejpam-5494	266	63	w2(x	w2(x	PROPN
ejpam-5494	266	64	,	,	PUNCT
ejpam-5494	266	65	y	y	PROPN
ejpam-5494	266	66	,	,	PUNCT
ejpam-5494	266	67	t	t	PROPN
ejpam-5494	266	68	)	)	PUNCT
ejpam-5494	266	69	when	when	SCONJ
ejpam-5494	266	70	x	x	X
ejpam-5494	266	71	=	=	PUNCT
ejpam-5494	266	72	y	y	PROPN
ejpam-5494	266	73	=	=	PUNCT
ejpam-5494	266	74	0.2	0.2	NUM
ejpam-5494	266	75	and	and	CCONJ
ejpam-5494	266	76	x	x	X
ejpam-5494	266	77	=	=	PUNCT
ejpam-5494	266	78	y	y	NOUN
ejpam-5494	266	79	=	=	SYM
ejpam-5494	266	80	0.5	0.5	NUM
ejpam-5494	266	81	in	in	ADP
ejpam-5494	266	82	example	example	NOUN
ejpam-5494	266	83	2	2	NUM
ejpam-5494	266	84	using	use	VERB
ejpam-5494	266	85	different	different	ADJ
ejpam-5494	266	86	t	t	NOUN
ejpam-5494	266	87	values	value	NOUN
ejpam-5494	267	1	.	.	PUNCT
ejpam-5494	268	1	(	(	PUNCT
ejpam-5494	268	2	x	x	X
ejpam-5494	268	3	,	,	PUNCT
ejpam-5494	268	4	y	y	PROPN
ejpam-5494	268	5	)	)	PUNCT
ejpam-5494	268	6	t	t	PROPN
ejpam-5494	268	7	w2(x	w2(x	PROPN
ejpam-5494	268	8	,	,	PUNCT
ejpam-5494	268	9	y	y	PROPN
ejpam-5494	268	10	,	,	PUNCT
ejpam-5494	268	11	t	t	PROPN
ejpam-5494	268	12	)	)	PUNCT
ejpam-5494	268	13	exact	exact	PROPN
ejpam-5494	268	14	soln	soln	NOUN
ejpam-5494	268	15	.	.	PUNCT
ejpam-5494	269	1	abs	ab	NOUN
ejpam-5494	269	2	.	.	PUNCT
ejpam-5494	270	1	error	error	NOUN
ejpam-5494	270	2	(	(	PUNCT
ejpam-5494	270	3	srpsm	srpsm	ADJ
ejpam-5494	270	4	)	)	PUNCT
ejpam-5494	270	5	abs	ab	NOUN
ejpam-5494	270	6	.	.	PUNCT
ejpam-5494	271	1	error	error	NOUN
ejpam-5494	271	2	(	(	PUNCT
ejpam-5494	271	3	crps)[6	crps)[6	X
ejpam-5494	271	4	]	]	X
ejpam-5494	271	5	0.2	0.2	NUM
ejpam-5494	271	6	1.648466291	1.648466291	NUM
ejpam-5494	271	7	1.648721271	1.648721271	NUM
ejpam-5494	271	8	2.54980×	2.54980×	NUM
ejpam-5494	271	9	10−4	10−4	NUM
ejpam-5494	271	10	2.5497×	2.5497×	NUM
ejpam-5494	271	11	10−4	10−4	NUM
ejpam-5494	271	12	(	(	PUNCT
ejpam-5494	271	13	0.2	0.2	NUM
ejpam-5494	271	14	,	,	PUNCT
ejpam-5494	271	15	0.2	0.2	NUM
ejpam-5494	271	16	)	)	PUNCT
ejpam-5494	271	17	0.4	0.4	NUM
ejpam-5494	272	1	1.820026132	1.820026132	NUM
ejpam-5494	272	2	1.822118800	1.822118800	NUM
ejpam-5494	272	3	2.092668×	2.092668×	NUM
ejpam-5494	272	4	10−3	10−3	NUM
ejpam-5494	272	5	2.0926×	2.0926×	NUM
ejpam-5494	272	6	10−3	10−3	NUM
ejpam-5494	272	7	0.6	0.6	NUM
ejpam-5494	272	8	2.006504218	2.006504218	NUM
ejpam-5494	272	9	2.013752707	2.013752707	NUM
ejpam-5494	272	10	7.248489×	7.248489×	NUM
ejpam-5494	272	11	10−3	10−3	NUM
ejpam-5494	272	12	7.2484×	7.2484×	NUM
ejpam-5494	272	13	10−3	10−3	NUM
ejpam-5494	272	14	0.8	0.8	NUM
ejpam-5494	272	15	2.207900553	2.207900553	NUM
ejpam-5494	272	16	2.225540928	2.225540928	NUM
ejpam-5494	272	17	1.7640375×	1.7640375×	NUM
ejpam-5494	272	18	10−2	10−2	NUM
ejpam-5494	272	19	1.7640×	1.7640×	NUM
ejpam-5494	272	20	10−2	10−2	NUM
ejpam-5494	272	21	0.2	0.2	NUM
ejpam-5494	272	22	3.003701420	3.003701420	NUM
ejpam-5494	272	23	3.004166024	3.004166024	NUM
ejpam-5494	272	24	4.64604×	4.64604×	NUM
ejpam-5494	272	25	10−4	10−4	NUM
ejpam-5494	272	26	4.6460×	4.6460×	NUM
ejpam-5494	272	27	10−4	10−4	NUM
ejpam-5494	272	28	(	(	PUNCT
ejpam-5494	272	29	0.5	0.5	NUM
ejpam-5494	272	30	,	,	PUNCT
ejpam-5494	272	31	0.5	0.5	NUM
ejpam-5494	272	32	)	)	PUNCT
ejpam-5494	272	33	0.4	0.4	NUM
ejpam-5494	272	34	3.316303831	3.316303831	NUM
ejpam-5494	272	35	3.320116923	3.320116923	NUM
ejpam-5494	272	36	3.813092×	3.813092×	NUM
ejpam-5494	272	37	10−3	10−3	NUM
ejpam-5494	272	38	3.8130×	3.8130×	NUM
ejpam-5494	272	39	10−3	10−3	NUM
ejpam-5494	272	40	0.6	0.6	NUM
ejpam-5494	272	41	3.656089058	3.656089058	NUM
ejpam-5494	272	42	3.669296668	3.669296668	NUM
ejpam-5494	272	43	1.3207610×	1.3207610×	NUM
ejpam-5494	272	44	10−2	10−2	NUM
ejpam-5494	272	45	1.3207×	1.3207×	NUM
ejpam-5494	272	46	10−3	10−3	NUM
ejpam-5494	272	47	0.8	0.8	NUM
ejpam-5494	272	48	4.023057105	4.023057105	NUM
ejpam-5494	272	49	4.055199967	4.055199967	NUM
ejpam-5494	272	50	3.2142862×	3.2142862×	NUM
ejpam-5494	272	51	10−2	10−2	NUM
ejpam-5494	272	52	3.2142×	3.2142×	NUM
ejpam-5494	272	53	10−2	10−2	NUM
ejpam-5494	273	1	p.	p.	NOUN
ejpam-5494	273	2	pue	pue	NOUN
ejpam-5494	273	3	-	-	PUNCT
ejpam-5494	273	4	on	on	ADP
ejpam-5494	273	5	/	/	SYM
ejpam-5494	273	6	eur	eur	NOUN
ejpam-5494	273	7	.	.	PUNCT
ejpam-5494	274	1	j.	j.	PROPN
ejpam-5494	274	2	pure	pure	PROPN
ejpam-5494	274	3	appl	appl	PROPN
ejpam-5494	274	4	.	.	PROPN
ejpam-5494	274	5	math	math	PROPN
ejpam-5494	274	6	,	,	PUNCT
ejpam-5494	274	7	17	17	NUM
ejpam-5494	274	8	(	(	PUNCT
ejpam-5494	274	9	4	4	NUM
ejpam-5494	274	10	)	)	PUNCT
ejpam-5494	274	11	(	(	PUNCT
ejpam-5494	274	12	2024	2024	NUM
ejpam-5494	274	13	)	)	PUNCT
ejpam-5494	274	14	,	,	PUNCT
ejpam-5494	274	15	3826	3826	NUM
ejpam-5494	274	16	-	-	SYM
ejpam-5494	274	17	3846	3846	NUM
ejpam-5494	274	18	3840	3840	NUM
ejpam-5494	274	19	figure	figure	NOUN
ejpam-5494	274	20	7	7	NUM
ejpam-5494	274	21	:	:	PUNCT
ejpam-5494	274	22	subplot	subplot	NOUN
ejpam-5494	274	23	(	(	PUNCT
ejpam-5494	274	24	a	a	X
ejpam-5494	274	25	)	)	PUNCT
ejpam-5494	274	26	depicts	depict	VERB
ejpam-5494	274	27	the	the	DET
ejpam-5494	274	28	approximate	approximate	ADJ
ejpam-5494	274	29	solution	solution	NOUN
ejpam-5494	274	30	u2(x	u2(x	PROPN
ejpam-5494	274	31	,	,	PUNCT
ejpam-5494	274	32	t	t	PROPN
ejpam-5494	274	33	)	)	PUNCT
ejpam-5494	274	34	and	and	CCONJ
ejpam-5494	274	35	subplot	subplot	NOUN
ejpam-5494	274	36	(	(	PUNCT
ejpam-5494	274	37	b	b	NOUN
ejpam-5494	274	38	)	)	PUNCT
ejpam-5494	274	39	presents	present	VERB
ejpam-5494	274	40	the	the	DET
ejpam-5494	274	41	approximate	approximate	ADJ
ejpam-5494	274	42	solution	solution	NOUN
ejpam-5494	274	43	w2(x	w2(x	PROPN
ejpam-5494	274	44	,	,	PUNCT
ejpam-5494	274	45	t	t	PROPN
ejpam-5494	274	46	)	)	PUNCT
ejpam-5494	274	47	for	for	ADP
ejpam-5494	274	48	example	example	NOUN
ejpam-5494	274	49	3	3	NUM
ejpam-5494	274	50	at	at	ADP
ejpam-5494	274	51	different	different	ADJ
ejpam-5494	274	52	γ	γ	NOUN
ejpam-5494	274	53	values	value	NOUN
ejpam-5494	274	54	for	for	ADP
ejpam-5494	274	55	x	x	SYM
ejpam-5494	274	56	=	=	SYM
ejpam-5494	274	57	0.5	0.5	NUM
ejpam-5494	274	58	.	.	PUNCT
ejpam-5494	274	59	example	example	NOUN
ejpam-5494	275	1	3	3	X
ejpam-5494	275	2	.	.	X
ejpam-5494	275	3	consider	consider	VERB
ejpam-5494	275	4	the	the	DET
ejpam-5494	275	5	coupled	couple	VERB
ejpam-5494	275	6	system	system	NOUN
ejpam-5494	275	7	of	of	ADP
ejpam-5494	275	8	reaction	reaction	NOUN
ejpam-5494	275	9	-	-	PUNCT
ejpam-5494	275	10	diffusion	diffusion	NOUN
ejpam-5494	275	11	equations	equation	NOUN
ejpam-5494	275	12	dγ	dγ	ADP
ejpam-5494	275	13	t	t	PROPN
ejpam-5494	275	14	u(x	u(x	PROPN
ejpam-5494	275	15	,	,	PUNCT
ejpam-5494	275	16	t	t	PROPN
ejpam-5494	275	17	)	)	PUNCT
ejpam-5494	275	18	=	=	SYM
ejpam-5494	275	19	u(x	u(x	PROPN
ejpam-5494	275	20	,	,	PUNCT
ejpam-5494	275	21	t)−	t)−	PROPN
ejpam-5494	275	22	u2(x	u2(x	PROPN
ejpam-5494	275	23	,	,	PUNCT
ejpam-5494	275	24	t)−	t)−	PROPN
ejpam-5494	275	25	u(x	u(x	NOUN
ejpam-5494	275	26	,	,	PUNCT
ejpam-5494	275	27	t)w(x	t)w(x	NOUN
ejpam-5494	275	28	,	,	PUNCT
ejpam-5494	275	29	t	t	PROPN
ejpam-5494	275	30	)	)	PUNCT
ejpam-5494	276	1	+	+	CCONJ
ejpam-5494	276	2	uxx(x	uxx(x	PROPN
ejpam-5494	276	3	,	,	PUNCT
ejpam-5494	276	4	t	t	PROPN
ejpam-5494	276	5	)	)	PUNCT
ejpam-5494	276	6	,	,	PUNCT
ejpam-5494	276	7	dγ	dγ	ADP
ejpam-5494	276	8	t	t	PROPN
ejpam-5494	276	9	w(x	w(x	PROPN
ejpam-5494	276	10	,	,	PUNCT
ejpam-5494	276	11	t	t	PROPN
ejpam-5494	276	12	)	)	PUNCT
ejpam-5494	277	1	=	=	SYM
ejpam-5494	277	2	wxx(x	wxx(x	PROPN
ejpam-5494	277	3	,	,	PUNCT
ejpam-5494	277	4	t)−	t)−	PROPN
ejpam-5494	277	5	u(x	u(x	NOUN
ejpam-5494	277	6	,	,	PUNCT
ejpam-5494	277	7	t)w(x	t)w(x	NOUN
ejpam-5494	277	8	,	,	PUNCT
ejpam-5494	277	9	t	t	PROPN
ejpam-5494	277	10	)	)	PUNCT
ejpam-5494	277	11	,	,	PUNCT
ejpam-5494	277	12	subject	subject	ADJ
ejpam-5494	277	13	to	to	ADP
ejpam-5494	277	14	the	the	DET
ejpam-5494	277	15	initial	initial	ADJ
ejpam-5494	277	16	conditions	condition	NOUN
ejpam-5494	277	17	u(x	u(x	NOUN
ejpam-5494	277	18	,	,	PUNCT
ejpam-5494	277	19	0	0	NUM
ejpam-5494	277	20	)	)	PUNCT
ejpam-5494	277	21	=	=	PRON
ejpam-5494	278	1	epx	epx	X
ejpam-5494	278	2	(	(	PUNCT
ejpam-5494	278	3	1	1	NUM
ejpam-5494	278	4	+	+	CCONJ
ejpam-5494	278	5	e0.5px)2	e0.5px)2	NOUN
ejpam-5494	278	6	,	,	PUNCT
ejpam-5494	278	7	w(x	w(x	PROPN
ejpam-5494	278	8	,	,	PUNCT
ejpam-5494	278	9	0	0	NUM
ejpam-5494	278	10	)	)	PUNCT
ejpam-5494	278	11	=	=	SYM
ejpam-5494	278	12	1	1	NUM
ejpam-5494	278	13	1	1	NUM
ejpam-5494	278	14	+	+	CCONJ
ejpam-5494	278	15	e0.5px	e0.5px	PROPN
ejpam-5494	278	16	where	where	SCONJ
ejpam-5494	278	17	p	p	NOUN
ejpam-5494	278	18	is	be	AUX
ejpam-5494	278	19	constant	constant	ADJ
ejpam-5494	278	20	.	.	PUNCT
ejpam-5494	279	1	here	here	ADV
ejpam-5494	279	2	n1(u	n1(u	NOUN
ejpam-5494	279	3	,	,	PUNCT
ejpam-5494	279	4	w	w	NOUN
ejpam-5494	279	5	)	)	PUNCT
ejpam-5494	279	6	=	=	SYM
ejpam-5494	279	7	u−u2−uw+ux	u−u2−uw+ux	PROPN
ejpam-5494	279	8	,	,	PUNCT
ejpam-5494	279	9	n2(u	n2(u	PROPN
ejpam-5494	279	10	,	,	PUNCT
ejpam-5494	279	11	w	w	NOUN
ejpam-5494	279	12	)	)	PUNCT
ejpam-5494	279	13	=	=	PUNCT
ejpam-5494	279	14	wxx−uw	wxx−uw	ADJ
ejpam-5494	279	15	,	,	PUNCT
ejpam-5494	279	16	f1(x	f1(x	PROPN
ejpam-5494	279	17	,	,	PUNCT
ejpam-5494	279	18	t	t	PROPN
ejpam-5494	279	19	)	)	PUNCT
ejpam-5494	279	20	=	=	SYM
ejpam-5494	280	1	f2(x	f2(x	PROPN
ejpam-5494	280	2	,	,	PUNCT
ejpam-5494	280	3	t	t	PROPN
ejpam-5494	280	4	)	)	PUNCT
ejpam-5494	280	5	=	=	SYM
ejpam-5494	280	6	0	0	NUM
ejpam-5494	280	7	,	,	PUNCT
ejpam-5494	280	8	g1(x	g1(x	NOUN
ejpam-5494	280	9	)	)	PUNCT
ejpam-5494	280	10	=	=	AUX
ejpam-5494	281	1	epx	epx	X
ejpam-5494	281	2	(	(	PUNCT
ejpam-5494	281	3	1+e0.5px)2	1+e0.5px)2	NUM
ejpam-5494	281	4	,	,	PUNCT
ejpam-5494	281	5	g2(x	g2(x	X
ejpam-5494	281	6	)	)	PUNCT
ejpam-5494	281	7	=	=	SYM
ejpam-5494	281	8	1	1	NUM
ejpam-5494	281	9	1+e0.5px	1+e0.5px	NUM
ejpam-5494	281	10	.	.	PUNCT
ejpam-5494	282	1	the	the	DET
ejpam-5494	282	2	kth−	kth−	PROPN
ejpam-5494	282	3	truncated	truncated	ADJ
ejpam-5494	282	4	term	term	NOUN
ejpam-5494	282	5	series	series	NOUN
ejpam-5494	282	6	solution	solution	NOUN
ejpam-5494	282	7	to	to	ADP
ejpam-5494	282	8	the	the	DET
ejpam-5494	282	9	problem	problem	NOUN
ejpam-5494	282	10	is	be	AUX
ejpam-5494	282	11	uk(x	uk(x	ADV
ejpam-5494	282	12	,	,	PUNCT
ejpam-5494	282	13	t	t	PROPN
ejpam-5494	282	14	)	)	PUNCT
ejpam-5494	282	15	=	=	PUNCT
ejpam-5494	282	16	k∑	k∑	PROPN
ejpam-5494	282	17	n=0	n=0	NUM
ejpam-5494	282	18	an(x	an(x	NOUN
ejpam-5494	282	19	)	)	PUNCT
ejpam-5494	282	20	tnγ	tnγ	NOUN
ejpam-5494	282	21	γ(nγ	γ(nγ	NOUN
ejpam-5494	282	22	+	+	CCONJ
ejpam-5494	282	23	1	1	X
ejpam-5494	282	24	)	)	PUNCT
ejpam-5494	282	25	and	and	CCONJ
ejpam-5494	282	26	wk(x	wk(x	NOUN
ejpam-5494	282	27	,	,	PUNCT
ejpam-5494	282	28	t	t	PROPN
ejpam-5494	282	29	)	)	PUNCT
ejpam-5494	282	30	=	=	PUNCT
ejpam-5494	283	1	k∑	k∑	PROPN
ejpam-5494	283	2	n=0	n=0	PROPN
ejpam-5494	283	3	bn(x	bn(x	X
ejpam-5494	283	4	)	)	PUNCT
ejpam-5494	283	5	tnγ	tnγ	NOUN
ejpam-5494	283	6	γ(nγ	γ(nγ	NOUN
ejpam-5494	283	7	+	+	CCONJ
ejpam-5494	283	8	1	1	NUM
ejpam-5494	283	9	)	)	PUNCT
ejpam-5494	283	10	.	.	PUNCT
ejpam-5494	284	1	the	the	DET
ejpam-5494	284	2	iteration	iteration	NOUN
ejpam-5494	284	3	for	for	ADP
ejpam-5494	284	4	this	this	DET
ejpam-5494	284	5	problem	problem	NOUN
ejpam-5494	284	6	is	be	AUX
ejpam-5494	284	7	u0(x	u0(x	NUM
ejpam-5494	284	8	,	,	PUNCT
ejpam-5494	284	9	t	t	PROPN
ejpam-5494	284	10	)	)	PUNCT
ejpam-5494	285	1	=	=	AUX
ejpam-5494	285	2	epx	epx	X
ejpam-5494	285	3	(	(	PUNCT
ejpam-5494	285	4	1	1	NUM
ejpam-5494	285	5	+	+	CCONJ
ejpam-5494	285	6	e0.5px)2	e0.5px)2	NOUN
ejpam-5494	285	7	,	,	PUNCT
ejpam-5494	285	8	w0(x	w0(x	PROPN
ejpam-5494	285	9	,	,	PUNCT
ejpam-5494	285	10	t	t	PROPN
ejpam-5494	285	11	)	)	PUNCT
ejpam-5494	285	12	=	=	SYM
ejpam-5494	285	13	1	1	NUM
ejpam-5494	285	14	1	1	NUM
ejpam-5494	285	15	+	+	CCONJ
ejpam-5494	285	16	e0.5px	e0.5px	PROPN
ejpam-5494	285	17	,	,	PUNCT
ejpam-5494	285	18	res1,k(x	res1,k(x	PROPN
ejpam-5494	285	19	,	,	PUNCT
ejpam-5494	285	20	t	t	PROPN
ejpam-5494	285	21	)	)	PUNCT
ejpam-5494	285	22	=	=	PUNCT
ejpam-5494	286	1	uk(x	uk(x	PROPN
ejpam-5494	286	2	,	,	PUNCT
ejpam-5494	286	3	t)−	t)−	PROPN
ejpam-5494	286	4	epx	epx	X
ejpam-5494	286	5	(	(	PUNCT
ejpam-5494	286	6	1	1	NUM
ejpam-5494	286	7	+	+	NOUN
ejpam-5494	286	8	e0.5px)2	e0.5px)2	NOUN
ejpam-5494	286	9	−	−	PROPN
ejpam-5494	286	10	s−1	s−1	PROPN
ejpam-5494	286	11	[	[	PUNCT
ejpam-5494	286	12	1	1	NUM
ejpam-5494	286	13	vγα	vγα	NOUN
ejpam-5494	286	14	s	s	X
ejpam-5494	286	15	[	[	PUNCT
ejpam-5494	286	16	uk−1	uk−1	PROPN
ejpam-5494	286	17	]	]	X
ejpam-5494	286	18	]	]	X
ejpam-5494	287	1	+	+	CCONJ
ejpam-5494	287	2	s−1	s−1	PROPN
ejpam-5494	287	3	[	[	PUNCT
ejpam-5494	287	4	1	1	NUM
ejpam-5494	287	5	vγα	vγα	NOUN
ejpam-5494	287	6	s	s	X
ejpam-5494	287	7	[	[	PUNCT
ejpam-5494	287	8	u2k−1	u2k−1	PROPN
ejpam-5494	287	9	]	]	X
ejpam-5494	287	10	]	]	X
ejpam-5494	288	1	+	+	CCONJ
ejpam-5494	288	2	s−1	s−1	PROPN
ejpam-5494	288	3	[	[	PUNCT
ejpam-5494	288	4	1	1	NUM
ejpam-5494	288	5	vγα	vγα	NOUN
ejpam-5494	288	6	s	s	X
ejpam-5494	288	7	[	[	PUNCT
ejpam-5494	288	8	uk−1wk−1	uk−1wk−1	X
ejpam-5494	288	9	]	]	X
ejpam-5494	288	10	]	]	X
ejpam-5494	288	11	−	−	PROPN
ejpam-5494	288	12	s−1	s−1	PROPN
ejpam-5494	288	13	[	[	PUNCT
ejpam-5494	288	14	1	1	NUM
ejpam-5494	288	15	vγα	vγα	NOUN
ejpam-5494	288	16	s	s	X
ejpam-5494	288	17	[	[	PUNCT
ejpam-5494	288	18	(	(	PUNCT
ejpam-5494	288	19	uk−1)xx	uk−1)xx	ADP
ejpam-5494	288	20	]	]	X
ejpam-5494	288	21	]	]	PUNCT
ejpam-5494	288	22	,	,	PUNCT
ejpam-5494	288	23	k	k	PROPN
ejpam-5494	288	24	⩾	⩾	PROPN
ejpam-5494	288	25	1	1	NUM
ejpam-5494	288	26	res2,k(x	res2,k(x	VERB
ejpam-5494	288	27	,	,	PUNCT
ejpam-5494	288	28	t	t	NOUN
ejpam-5494	288	29	)	)	PUNCT
ejpam-5494	288	30	=	=	SYM
ejpam-5494	288	31	wk(x	wk(x	NOUN
ejpam-5494	288	32	,	,	PUNCT
ejpam-5494	289	1	t)−	t)−	PROPN
ejpam-5494	289	2	1	1	NUM
ejpam-5494	289	3	1	1	NUM
ejpam-5494	289	4	+	+	CCONJ
ejpam-5494	289	5	e0.5px	e0.5px	PROPN
ejpam-5494	289	6	−	−	PROPN
ejpam-5494	289	7	s−1	s−1	PROPN
ejpam-5494	289	8	[	[	PUNCT
ejpam-5494	289	9	1	1	NUM
ejpam-5494	289	10	vγα	vγα	NOUN
ejpam-5494	289	11	s	s	X
ejpam-5494	289	12	[	[	PUNCT
ejpam-5494	289	13	(	(	PUNCT
ejpam-5494	289	14	wk−1)xx	wk−1)xx	X
ejpam-5494	289	15	]	]	PUNCT
ejpam-5494	289	16	]	]	X
ejpam-5494	290	1	+	+	CCONJ
ejpam-5494	290	2	s−1	s−1	PROPN
ejpam-5494	290	3	[	[	PUNCT
ejpam-5494	290	4	1	1	NUM
ejpam-5494	290	5	vγα	vγα	NOUN
ejpam-5494	290	6	s	s	X
ejpam-5494	290	7	[	[	PUNCT
ejpam-5494	290	8	uk−1wk−1	uk−1wk−1	X
ejpam-5494	290	9	]	]	X
ejpam-5494	290	10	]	]	X
ejpam-5494	290	11	k	k	X
ejpam-5494	290	12	⩾	⩾	NOUN
ejpam-5494	290	13	1	1	X
ejpam-5494	290	14	.	.	PUNCT
ejpam-5494	291	1	after	after	ADP
ejpam-5494	291	2	a	a	DET
ejpam-5494	291	3	few	few	ADJ
ejpam-5494	291	4	iterations	iteration	NOUN
ejpam-5494	291	5	,	,	PUNCT
ejpam-5494	291	6	the	the	DET
ejpam-5494	291	7	coefficients	coefficient	NOUN
ejpam-5494	291	8	are	be	AUX
ejpam-5494	291	9	obtained	obtain	VERB
ejpam-5494	291	10	:	:	PUNCT
ejpam-5494	291	11	a1(x	a1(x	NOUN
ejpam-5494	291	12	)	)	PUNCT
ejpam-5494	292	1	=	=	AUX
ejpam-5494	292	2	epx	epx	X
ejpam-5494	292	3	(	(	PUNCT
ejpam-5494	292	4	1	1	NUM
ejpam-5494	292	5	+	+	CCONJ
ejpam-5494	292	6	e0.5px)4	e0.5px)4	ADJ
ejpam-5494	292	7	[	[	PUNCT
ejpam-5494	292	8	e0.5px	e0.5px	PROPN
ejpam-5494	292	9	−	−	PROPN
ejpam-5494	292	10	0.5p2e0.5px	0.5p2e0.5px	NOUN
ejpam-5494	293	1	+	+	CCONJ
ejpam-5494	293	2	p2	p2	PROPN
ejpam-5494	293	3	]	]	PUNCT
ejpam-5494	293	4	,	,	PUNCT
ejpam-5494	293	5	p.	p.	NOUN
ejpam-5494	293	6	pue	pue	NOUN
ejpam-5494	293	7	-	-	PUNCT
ejpam-5494	293	8	on	on	ADP
ejpam-5494	293	9	/	/	SYM
ejpam-5494	293	10	eur	eur	NOUN
ejpam-5494	293	11	.	.	PUNCT
ejpam-5494	294	1	j.	j.	PROPN
ejpam-5494	294	2	pure	pure	PROPN
ejpam-5494	294	3	appl	appl	PROPN
ejpam-5494	294	4	.	.	PROPN
ejpam-5494	294	5	math	math	PROPN
ejpam-5494	294	6	,	,	PUNCT
ejpam-5494	294	7	17	17	NUM
ejpam-5494	294	8	(	(	PUNCT
ejpam-5494	294	9	4	4	NUM
ejpam-5494	294	10	)	)	PUNCT
ejpam-5494	294	11	(	(	PUNCT
ejpam-5494	294	12	2024	2024	NUM
ejpam-5494	294	13	)	)	PUNCT
ejpam-5494	294	14	,	,	PUNCT
ejpam-5494	294	15	3826	3826	NUM
ejpam-5494	294	16	-	-	SYM
ejpam-5494	294	17	3846	3846	NUM
ejpam-5494	294	18	3841	3841	NUM
ejpam-5494	294	19	b1(x	b1(x	NOUN
ejpam-5494	294	20	)	)	PUNCT
ejpam-5494	294	21	=	=	NUM
ejpam-5494	294	22	0.25	0.25	NUM
ejpam-5494	294	23	(	(	PUNCT
ejpam-5494	294	24	1	1	NUM
ejpam-5494	294	25	+	+	NUM
ejpam-5494	294	26	e0.5px)3	e0.5px)3	NOUN
ejpam-5494	294	27	[	[	PUNCT
ejpam-5494	294	28	p2epx	p2epx	ADP
ejpam-5494	294	29	−	−	ADP
ejpam-5494	294	30	4epx	4epx	DET
ejpam-5494	294	31	−	−	PROPN
ejpam-5494	294	32	p2e0.5px	p2e0.5px	NOUN
ejpam-5494	294	33	]	]	PUNCT
ejpam-5494	294	34	,	,	PUNCT
ejpam-5494	294	35	and	and	CCONJ
ejpam-5494	294	36	a2(x	a2(x	PROPN
ejpam-5494	294	37	)	)	PUNCT
ejpam-5494	294	38	=	=	SYM
ejpam-5494	294	39	1	1	NUM
ejpam-5494	294	40	8(1	8(1	NOUN
ejpam-5494	294	41	+	+	CCONJ
ejpam-5494	294	42	e0.5px)6	e0.5px)6	VERB
ejpam-5494	294	43	[	[	PUNCT
ejpam-5494	294	44	−	−	PROPN
ejpam-5494	294	45	32p2e2px	32p2e2px	NUM
ejpam-5494	295	1	+	+	SYM
ejpam-5494	295	2	16e2px	16e2px	NUM
ejpam-5494	296	1	+	+	CCONJ
ejpam-5494	296	2	28p2e1.5px	28p2e1.5px	NUM
ejpam-5494	296	3	−	−	PROPN
ejpam-5494	296	4	33p4e1.5px	33p4e1.5px	NUM
ejpam-5494	296	5	+	+	SYM
ejpam-5494	296	6	4p2e2.5px	4p2e2.5px	NUM
ejpam-5494	297	1	+	+	NUM
ejpam-5494	297	2	18p4e2px	18p4e2px	NUM
ejpam-5494	298	1	−	−	PROPN
ejpam-5494	298	2	p4e2.5px	p4e2.5px	NOUN
ejpam-5494	298	3	+	+	CCONJ
ejpam-5494	298	4	8p4epx	8p4epx	PROPN
ejpam-5494	298	5	]	]	PUNCT
ejpam-5494	298	6	,	,	PUNCT
ejpam-5494	298	7	b2(x	b2(x	X
ejpam-5494	298	8	)	)	PUNCT
ejpam-5494	298	9	=	=	SYM
ejpam-5494	298	10	1	1	NUM
ejpam-5494	298	11	16(1	16(1	NUM
ejpam-5494	298	12	+	+	ADJ
ejpam-5494	298	13	e0.5px)5	e0.5px)5	ADV
ejpam-5494	298	14	[	[	PUNCT
ejpam-5494	298	15	p4e2px	p4e2px	X
ejpam-5494	298	16	+	+	X
ejpam-5494	298	17	16e2px	16e2px	ADJ
ejpam-5494	298	18	−	−	NOUN
ejpam-5494	298	19	8p2e2px	8p2e2px	NUM
ejpam-5494	298	20	+	+	CCONJ
ejpam-5494	298	21	11p4epx	11p4epx	NUM
ejpam-5494	299	1	−	−	NUM
ejpam-5494	299	2	11p4e1.5px	11p4e1.5px	NUM
ejpam-5494	299	3	+	+	CCONJ
ejpam-5494	299	4	40p2e1.5px	40p2e1.5px	ADJ
ejpam-5494	299	5	−	−	NOUN
ejpam-5494	299	6	p4e0.5px	p4e0.5px	NOUN
ejpam-5494	299	7	−	−	PROPN
ejpam-5494	299	8	32p2epx	32p2epx	NUM
ejpam-5494	299	9	−	−	PROPN
ejpam-5494	299	10	16e1.5px	16e1.5px	NUM
ejpam-5494	299	11	]	]	PUNCT
ejpam-5494	299	12	,	,	PUNCT
ejpam-5494	299	13	hence	hence	ADV
ejpam-5494	299	14	,	,	PUNCT
ejpam-5494	299	15	the	the	DET
ejpam-5494	299	16	2	2	NUM
ejpam-5494	299	17	-	-	PUNCT
ejpam-5494	299	18	nd	nd	NOUN
ejpam-5494	299	19	order	order	NOUN
ejpam-5494	299	20	approximate	approximate	ADJ
ejpam-5494	299	21	solution	solution	NOUN
ejpam-5494	299	22	is	be	AUX
ejpam-5494	299	23	table	table	NOUN
ejpam-5494	299	24	7	7	NUM
ejpam-5494	299	25	:	:	PUNCT
ejpam-5494	299	26	comparison	comparison	NOUN
ejpam-5494	299	27	of	of	ADP
ejpam-5494	299	28	the	the	DET
ejpam-5494	299	29	approximate	approximate	ADJ
ejpam-5494	299	30	solution	solution	NOUN
ejpam-5494	299	31	u2(x	u2(x	PROPN
ejpam-5494	299	32	,	,	PUNCT
ejpam-5494	299	33	t	t	PROPN
ejpam-5494	299	34	)	)	PUNCT
ejpam-5494	299	35	in	in	ADP
ejpam-5494	299	36	example	example	NOUN
ejpam-5494	299	37	3	3	NUM
ejpam-5494	299	38	using	use	VERB
ejpam-5494	299	39	different	different	ADJ
ejpam-5494	299	40	γ	γ	NOUN
ejpam-5494	299	41	values	value	NOUN
ejpam-5494	299	42	.	.	PUNCT
ejpam-5494	300	1	t	t	NOUN
ejpam-5494	300	2	x	x	PUNCT
ejpam-5494	300	3	γ	γ	X
ejpam-5494	300	4	=	=	SYM
ejpam-5494	300	5	0.2	0.2	NUM
ejpam-5494	300	6	γ	γ	X
ejpam-5494	300	7	=	=	SYM
ejpam-5494	300	8	0.4	0.4	NUM
ejpam-5494	300	9	γ	γ	X
ejpam-5494	300	10	=	=	SYM
ejpam-5494	300	11	0.6	0.6	NUM
ejpam-5494	300	12	γ	γ	X
ejpam-5494	300	13	=	=	NOUN
ejpam-5494	300	14	0.8	0.8	NUM
ejpam-5494	300	15	γ	γ	X
ejpam-5494	300	16	=	=	SYM
ejpam-5494	300	17	1	1	NUM
ejpam-5494	300	18	0.2	0.2	NUM
ejpam-5494	300	19	0.3346368216	0.3346368216	NUM
ejpam-5494	300	20	0.3075765318	0.3075765318	NUM
ejpam-5494	300	21	0.2909673743	0.2909673743	NUM
ejpam-5494	300	22	0.2809869555	0.2809869555	NUM
ejpam-5494	300	23	0.2750395108	0.2750395108	NUM
ejpam-5494	300	24	0.4	0.4	NUM
ejpam-5494	300	25	0.3545182352	0.3545182352	NUM
ejpam-5494	300	26	0.3265194339	0.3265194339	NUM
ejpam-5494	301	1	0.3093155911	0.3093155911	NUM
ejpam-5494	301	2	0.2989687897	0.2989687897	NUM
ejpam-5494	301	3	0.2927994540	0.2927994540	NUM
ejpam-5494	301	4	0.1	0.1	NUM
ejpam-5494	301	5	0.6	0.6	NUM
ejpam-5494	301	6	0.3747087628	0.3747087628	NUM
ejpam-5494	301	7	0.3458387005	0.3458387005	NUM
ejpam-5494	301	8	0.3280801409	0.3280801409	NUM
ejpam-5494	301	9	0.3173903381	0.3173903381	NUM
ejpam-5494	301	10	0.3110127944	0.3110127944	NUM
ejpam-5494	301	11	0.8	0.8	NUM
ejpam-5494	301	12	0.3951398996	0.3951398996	NUM
ejpam-5494	301	13	0.3654736576	0.3654736576	NUM
ejpam-5494	301	14	0.3472053559	0.3472053559	NUM
ejpam-5494	301	15	0.3361990391	0.3361990391	NUM
ejpam-5494	301	16	0.3296288598	0.3296288598	NUM
ejpam-5494	301	17	1.0	1.0	NUM
ejpam-5494	301	18	0.4157415419	0.4157415419	NUM
ejpam-5494	301	19	0.3853612031	0.3853612031	NUM
ejpam-5494	301	20	0.3666326584	0.3666326584	NUM
ejpam-5494	301	21	0.3553391449	0.3553391449	NUM
ejpam-5494	301	22	0.3485936321	0.3485936321	NUM
ejpam-5494	301	23	table	table	NOUN
ejpam-5494	301	24	8	8	NUM
ejpam-5494	301	25	:	:	PUNCT
ejpam-5494	301	26	comparison	comparison	NOUN
ejpam-5494	301	27	of	of	ADP
ejpam-5494	301	28	the	the	DET
ejpam-5494	301	29	approximate	approximate	ADJ
ejpam-5494	301	30	solution	solution	NOUN
ejpam-5494	301	31	w2(x	w2(x	PROPN
ejpam-5494	301	32	,	,	PUNCT
ejpam-5494	301	33	t	t	PROPN
ejpam-5494	301	34	)	)	PUNCT
ejpam-5494	301	35	in	in	ADP
ejpam-5494	301	36	example	example	NOUN
ejpam-5494	301	37	3	3	NUM
ejpam-5494	301	38	using	use	VERB
ejpam-5494	301	39	different	different	ADJ
ejpam-5494	301	40	γ	γ	NOUN
ejpam-5494	301	41	values	value	NOUN
ejpam-5494	301	42	.	.	PUNCT
ejpam-5494	302	1	t	t	NOUN
ejpam-5494	302	2	x	x	PUNCT
ejpam-5494	302	3	γ	γ	X
ejpam-5494	302	4	=	=	SYM
ejpam-5494	302	5	0.2	0.2	NUM
ejpam-5494	302	6	γ	γ	X
ejpam-5494	302	7	=	=	SYM
ejpam-5494	302	8	0.4	0.4	NUM
ejpam-5494	302	9	γ	γ	X
ejpam-5494	302	10	=	=	SYM
ejpam-5494	302	11	0.6	0.6	NUM
ejpam-5494	302	12	γ	γ	X
ejpam-5494	302	13	=	=	NOUN
ejpam-5494	302	14	0.8	0.8	NUM
ejpam-5494	302	15	γ	γ	X
ejpam-5494	302	16	=	=	SYM
ejpam-5494	302	17	1	1	NUM
ejpam-5494	302	18	0.2	0.2	NUM
ejpam-5494	302	19	0.3968241630	0.3968241630	NUM
ejpam-5494	303	1	0.4264368572	0.4264368572	NUM
ejpam-5494	303	2	0.4475212727	0.4475212727	NUM
ejpam-5494	303	3	0.4616009993	0.4616009993	NUM
ejpam-5494	303	4	0.4705466352	0.4705466352	NUM
ejpam-5494	303	5	0.4	0.4	NUM
ejpam-5494	303	6	0.3798767149	0.3798767149	NUM
ejpam-5494	303	7	0.4091653431	0.4091653431	NUM
ejpam-5494	303	8	0.4303163383	0.4303163383	NUM
ejpam-5494	303	9	0.4445647827	0.4445647827	NUM
ejpam-5494	303	10	0.4536616511	0.4536616511	NUM
ejpam-5494	303	11	0.1	0.1	NUM
ejpam-5494	303	12	0.6	0.6	NUM
ejpam-5494	303	13	0.3632965320	0.3632965320	NUM
ejpam-5494	303	14	0.3921407562	0.3921407562	NUM
ejpam-5494	303	15	0.4132861957	0.4132861957	NUM
ejpam-5494	303	16	0.4276608484	0.4276608484	NUM
ejpam-5494	303	17	0.4368839467	0.4368839467	NUM
ejpam-5494	303	18	0.8	0.8	NUM
ejpam-5494	303	19	0.3471168287	0.3471168287	NUM
ejpam-5494	303	20	0.3754019837	0.3754019837	NUM
ejpam-5494	303	21	0.3964705401	0.3964705401	NUM
ejpam-5494	303	22	0.4109280813	0.4109280813	NUM
ejpam-5494	303	23	0.4202514134	0.4202514134	NUM
ejpam-5494	303	24	1.0	1.0	NUM
ejpam-5494	303	25	0.3313660940	0.3313660940	NUM
ejpam-5494	303	26	0.3589848110	0.3589848110	NUM
ejpam-5494	303	27	0.3799068930	0.3799068930	NUM
ejpam-5494	303	28	0.3944037158	0.3944037158	NUM
ejpam-5494	303	29	0.4038005919	0.4038005919	NUM
ejpam-5494	303	30	u2(x	u2(x	PROPN
ejpam-5494	303	31	,	,	PUNCT
ejpam-5494	303	32	t	t	PROPN
ejpam-5494	303	33	)	)	PUNCT
ejpam-5494	303	34	=	=	AUX
ejpam-5494	304	1	epx	epx	X
ejpam-5494	304	2	(	(	PUNCT
ejpam-5494	304	3	1	1	NUM
ejpam-5494	304	4	+	+	CCONJ
ejpam-5494	304	5	e0.5px)2	e0.5px)2	NOUN
ejpam-5494	304	6	+	+	CCONJ
ejpam-5494	304	7	epx(e0.5px	epx(e0.5px	NOUN
ejpam-5494	304	8	−	−	NOUN
ejpam-5494	304	9	0.5p2e0.5px	0.5p2e0.5px	NOUN
ejpam-5494	305	1	+	+	CCONJ
ejpam-5494	305	2	p2	p2	NOUN
ejpam-5494	305	3	)	)	PUNCT
ejpam-5494	305	4	(	(	PUNCT
ejpam-5494	305	5	1	1	NUM
ejpam-5494	305	6	+	+	CCONJ
ejpam-5494	305	7	e0.5px)4	e0.5px)4	ADJ
ejpam-5494	305	8	·	·	PUNCT
ejpam-5494	305	9	tγ	tγ	PROPN
ejpam-5494	305	10	γ(γ	γ(γ	PROPN
ejpam-5494	305	11	+	+	CCONJ
ejpam-5494	305	12	1	1	X
ejpam-5494	305	13	)	)	PUNCT
ejpam-5494	305	14	+	+	CCONJ
ejpam-5494	305	15	(	(	PUNCT
ejpam-5494	305	16	18p4e2px	18p4e2px	NUM
ejpam-5494	305	17	−	−	NOUN
ejpam-5494	305	18	32p2e2px	32p2e2px	NUM
ejpam-5494	306	1	+	+	CCONJ
ejpam-5494	306	2	16e2px	16e2px	NUM
ejpam-5494	307	1	+	+	CCONJ
ejpam-5494	307	2	28p2e1.5px	28p2e1.5px	NUM
ejpam-5494	307	3	−	−	PROPN
ejpam-5494	307	4	33p4e1.5px	33p4e1.5px	NUM
ejpam-5494	307	5	+	+	CCONJ
ejpam-5494	307	6	4p2e2.5px	4p2e2.5px	NUM
ejpam-5494	307	7	−	−	PROPN
ejpam-5494	307	8	p4e2.5px	p4e2.5px	NOUN
ejpam-5494	307	9	+	+	CCONJ
ejpam-5494	307	10	8p4epx	8p4epx	NUM
ejpam-5494	307	11	)	)	PUNCT
ejpam-5494	307	12	8(1	8(1	NOUN
ejpam-5494	307	13	+	+	CCONJ
ejpam-5494	307	14	e0.5px)6	e0.5px)6	VERB
ejpam-5494	307	15	×	×	PROPN
ejpam-5494	307	16	t2γ	t2γ	NOUN
ejpam-5494	307	17	γ(2γ	γ(2γ	NOUN
ejpam-5494	307	18	+	+	NOUN
ejpam-5494	307	19	1	1	NUM
ejpam-5494	307	20	)	)	PUNCT
ejpam-5494	307	21	,	,	PUNCT
ejpam-5494	307	22	w2(x	w2(x	PROPN
ejpam-5494	307	23	,	,	PUNCT
ejpam-5494	307	24	t	t	PROPN
ejpam-5494	307	25	)	)	PUNCT
ejpam-5494	307	26	=	=	SYM
ejpam-5494	307	27	1	1	NUM
ejpam-5494	307	28	1	1	NUM
ejpam-5494	307	29	+	+	CCONJ
ejpam-5494	307	30	e0.5px	e0.5px	PROPN
ejpam-5494	307	31	+	+	CCONJ
ejpam-5494	307	32	0.25(p2epx	0.25(p2epx	NUM
ejpam-5494	307	33	−	−	NOUN
ejpam-5494	307	34	4epx	4epx	NUM
ejpam-5494	307	35	−	−	PROPN
ejpam-5494	307	36	p2e0.5px	p2e0.5px	NOUN
ejpam-5494	307	37	)	)	PUNCT
ejpam-5494	307	38	(	(	PUNCT
ejpam-5494	307	39	1	1	NUM
ejpam-5494	307	40	+	+	NUM
ejpam-5494	307	41	e0.5px)3	e0.5px)3	NOUN
ejpam-5494	307	42	·	·	PUNCT
ejpam-5494	307	43	tγ	tγ	NOUN
ejpam-5494	307	44	γ(γ	γ(γ	PROPN
ejpam-5494	307	45	+	+	CCONJ
ejpam-5494	307	46	1	1	X
ejpam-5494	307	47	)	)	PUNCT
ejpam-5494	307	48	+	+	CCONJ
ejpam-5494	307	49	(	(	PUNCT
ejpam-5494	307	50	p4e2px	p4e2px	X
ejpam-5494	307	51	+	+	NUM
ejpam-5494	307	52	16e2px	16e2px	ADJ
ejpam-5494	307	53	−	−	NOUN
ejpam-5494	307	54	8p2e2px	8p2e2px	NUM
ejpam-5494	307	55	+	+	CCONJ
ejpam-5494	307	56	11p4epx	11p4epx	NUM
ejpam-5494	308	1	−	−	NUM
ejpam-5494	308	2	11p4e1.5px	11p4e1.5px	NUM
ejpam-5494	308	3	+	+	CCONJ
ejpam-5494	308	4	40p2e1.5px	40p2e1.5px	ADJ
ejpam-5494	308	5	−	−	NOUN
ejpam-5494	308	6	p4e0.5px	p4e0.5px	NOUN
ejpam-5494	308	7	−	−	PROPN
ejpam-5494	308	8	32p2epx	32p2epx	NUM
ejpam-5494	308	9	−	−	PROPN
ejpam-5494	308	10	16e1.5px	16e1.5px	NUM
ejpam-5494	308	11	)	)	PUNCT
ejpam-5494	308	12	16(1	16(1	PROPN
ejpam-5494	309	1	+	+	CCONJ
ejpam-5494	309	2	e0.5px)5	e0.5px)5	ADV
ejpam-5494	309	3	×	×	PROPN
ejpam-5494	309	4	t2γ	t2γ	NOUN
ejpam-5494	309	5	γ(2γ	γ(2γ	NOUN
ejpam-5494	309	6	+	+	NOUN
ejpam-5494	309	7	1	1	NUM
ejpam-5494	309	8	)	)	PUNCT
ejpam-5494	309	9	.	.	PUNCT
ejpam-5494	310	1	p.	p.	NOUN
ejpam-5494	310	2	pue	pue	NOUN
ejpam-5494	310	3	-	-	PUNCT
ejpam-5494	310	4	on	on	ADP
ejpam-5494	310	5	/	/	SYM
ejpam-5494	310	6	eur	eur	NOUN
ejpam-5494	310	7	.	.	PUNCT
ejpam-5494	311	1	j.	j.	PROPN
ejpam-5494	311	2	pure	pure	PROPN
ejpam-5494	311	3	appl	appl	PROPN
ejpam-5494	311	4	.	.	PROPN
ejpam-5494	311	5	math	math	PROPN
ejpam-5494	311	6	,	,	PUNCT
ejpam-5494	311	7	17	17	NUM
ejpam-5494	311	8	(	(	PUNCT
ejpam-5494	311	9	4	4	NUM
ejpam-5494	311	10	)	)	PUNCT
ejpam-5494	311	11	(	(	PUNCT
ejpam-5494	311	12	2024	2024	NUM
ejpam-5494	311	13	)	)	PUNCT
ejpam-5494	311	14	,	,	PUNCT
ejpam-5494	311	15	3826	3826	NUM
ejpam-5494	311	16	-	-	SYM
ejpam-5494	311	17	3846	3846	NUM
ejpam-5494	311	18	3842	3842	NUM
ejpam-5494	311	19	the	the	DET
ejpam-5494	311	20	approximate	approximate	ADJ
ejpam-5494	311	21	solution	solution	NOUN
ejpam-5494	311	22	for	for	ADP
ejpam-5494	311	23	example	example	NOUN
ejpam-5494	311	24	3	3	NUM
ejpam-5494	311	25	where	where	SCONJ
ejpam-5494	311	26	p	p	NOUN
ejpam-5494	311	27	=	=	SYM
ejpam-5494	311	28	2/3	2/3	NUM
ejpam-5494	311	29	are	be	AUX
ejpam-5494	311	30	shown	show	VERB
ejpam-5494	311	31	in	in	ADP
ejpam-5494	311	32	figure	figure	NOUN
ejpam-5494	311	33	7	7	NUM
ejpam-5494	311	34	.	.	PUNCT
ejpam-5494	311	35	figures	figure	NOUN
ejpam-5494	311	36	8	8	NUM
ejpam-5494	311	37	and	and	CCONJ
ejpam-5494	311	38	9	9	NUM
ejpam-5494	311	39	provide	provide	VERB
ejpam-5494	311	40	the	the	DET
ejpam-5494	311	41	visualizations	visualization	NOUN
ejpam-5494	311	42	to	to	ADP
ejpam-5494	311	43	the	the	DET
ejpam-5494	311	44	approximate	approximate	ADJ
ejpam-5494	311	45	solutions	solution	NOUN
ejpam-5494	311	46	.	.	PUNCT
ejpam-5494	312	1	figure	figure	VERB
ejpam-5494	312	2	8	8	NUM
ejpam-5494	312	3	:	:	PUNCT
ejpam-5494	312	4	the	the	DET
ejpam-5494	312	5	graphics	graphic	NOUN
ejpam-5494	312	6	represent	represent	VERB
ejpam-5494	312	7	the	the	DET
ejpam-5494	312	8	approximate	approximate	ADJ
ejpam-5494	312	9	solution	solution	NOUN
ejpam-5494	312	10	u2(x	u2(x	PROPN
ejpam-5494	312	11	,	,	PUNCT
ejpam-5494	312	12	t	t	PROPN
ejpam-5494	312	13	)	)	PUNCT
ejpam-5494	312	14	with	with	ADP
ejpam-5494	312	15	different	different	ADJ
ejpam-5494	312	16	γ	γ	NOUN
ejpam-5494	312	17	values	value	NOUN
ejpam-5494	312	18	:	:	PUNCT
ejpam-5494	312	19	(	(	PUNCT
ejpam-5494	312	20	a	a	X
ejpam-5494	312	21	)	)	PUNCT
ejpam-5494	312	22	γ	γ	NOUN
ejpam-5494	312	23	=	=	SYM
ejpam-5494	312	24	0.4	0.4	NUM
ejpam-5494	312	25	,	,	PUNCT
ejpam-5494	312	26	(	(	PUNCT
ejpam-5494	312	27	b	b	X
ejpam-5494	312	28	)	)	PUNCT
ejpam-5494	312	29	γ	γ	NOUN
ejpam-5494	312	30	=	=	SYM
ejpam-5494	312	31	0.6	0.6	NUM
ejpam-5494	312	32	,	,	PUNCT
ejpam-5494	312	33	(	(	PUNCT
ejpam-5494	312	34	c	c	X
ejpam-5494	312	35	)	)	PUNCT
ejpam-5494	312	36	γ	γ	NOUN
ejpam-5494	312	37	=	=	NUM
ejpam-5494	312	38	0.8	0.8	NUM
ejpam-5494	312	39	,	,	PUNCT
ejpam-5494	312	40	and	and	CCONJ
ejpam-5494	312	41	(	(	PUNCT
ejpam-5494	312	42	d	d	X
ejpam-5494	312	43	)	)	PUNCT
ejpam-5494	312	44	γ	γ	NOUN
ejpam-5494	312	45	=	=	SYM
ejpam-5494	312	46	1.0	1.0	NUM
ejpam-5494	312	47	for	for	ADP
ejpam-5494	312	48	example	example	NOUN
ejpam-5494	312	49	3	3	NUM
ejpam-5494	312	50	.	.	NOUN
ejpam-5494	312	51	4	4	NUM
ejpam-5494	312	52	.	.	X
ejpam-5494	312	53	discussion	discussion	NOUN
ejpam-5494	312	54	based	base	VERB
ejpam-5494	312	55	on	on	ADP
ejpam-5494	312	56	the	the	DET
ejpam-5494	312	57	findings	finding	NOUN
ejpam-5494	312	58	in	in	ADP
ejpam-5494	312	59	example	example	NOUN
ejpam-5494	312	60	1	1	NUM
ejpam-5494	312	61	,	,	PUNCT
ejpam-5494	312	62	the	the	DET
ejpam-5494	312	63	suggested	suggest	VERB
ejpam-5494	312	64	method	method	NOUN
ejpam-5494	312	65	provides	provide	VERB
ejpam-5494	312	66	a	a	DET
ejpam-5494	312	67	solution	solution	NOUN
ejpam-5494	312	68	in	in	ADP
ejpam-5494	312	69	the	the	DET
ejpam-5494	312	70	form	form	NOUN
ejpam-5494	312	71	of	of	ADP
ejpam-5494	312	72	an	an	DET
ejpam-5494	312	73	infinite	infinite	ADJ
ejpam-5494	312	74	series	series	NOUN
ejpam-5494	312	75	that	that	PRON
ejpam-5494	312	76	converges	converge	VERB
ejpam-5494	312	77	to	to	ADP
ejpam-5494	312	78	exact	exact	ADJ
ejpam-5494	312	79	solutions	solution	NOUN
ejpam-5494	312	80	.	.	PUNCT
ejpam-5494	313	1	figure	figure	NOUN
ejpam-5494	313	2	1	1	NUM
ejpam-5494	313	3	compares	compare	VERB
ejpam-5494	313	4	the	the	DET
ejpam-5494	313	5	approximate	approximate	ADJ
ejpam-5494	313	6	solutions	solution	NOUN
ejpam-5494	313	7	at	at	ADP
ejpam-5494	313	8	different	different	ADJ
ejpam-5494	313	9	γ	γ	NOUN
ejpam-5494	313	10	values	value	NOUN
ejpam-5494	313	11	with	with	ADP
ejpam-5494	313	12	the	the	DET
ejpam-5494	313	13	exact	exact	ADJ
ejpam-5494	313	14	solutions	solution	NOUN
ejpam-5494	313	15	when	when	SCONJ
ejpam-5494	313	16	x	x	PROPN
ejpam-5494	313	17	=	=	SYM
ejpam-5494	313	18	0.5	0.5	NUM
ejpam-5494	313	19	.	.	PUNCT
ejpam-5494	313	20	figures	figure	NOUN
ejpam-5494	313	21	2	2	NUM
ejpam-5494	313	22	and	and	CCONJ
ejpam-5494	313	23	3	3	NUM
ejpam-5494	313	24	compare	compare	VERB
ejpam-5494	313	25	the	the	DET
ejpam-5494	313	26	visualizations	visualization	NOUN
ejpam-5494	313	27	to	to	ADP
ejpam-5494	313	28	the	the	DET
ejpam-5494	313	29	approximate	approximate	ADJ
ejpam-5494	313	30	and	and	CCONJ
ejpam-5494	313	31	exact	exact	ADJ
ejpam-5494	313	32	solutions	solution	NOUN
ejpam-5494	313	33	.	.	PUNCT
ejpam-5494	314	1	these	these	DET
ejpam-5494	314	2	graphs	graph	NOUN
ejpam-5494	314	3	show	show	VERB
ejpam-5494	314	4	how	how	SCONJ
ejpam-5494	314	5	the	the	DET
ejpam-5494	314	6	solution	solution	NOUN
ejpam-5494	314	7	shapes	shape	NOUN
ejpam-5494	314	8	will	will	AUX
ejpam-5494	314	9	approach	approach	VERB
ejpam-5494	314	10	the	the	DET
ejpam-5494	314	11	precise	precise	ADJ
ejpam-5494	314	12	solution	solution	NOUN
ejpam-5494	314	13	as	as	ADP
ejpam-5494	314	14	gamma	gamma	NOUN
ejpam-5494	314	15	approaches	approach	VERB
ejpam-5494	314	16	1	1	NUM
ejpam-5494	314	17	.	.	PUNCT
ejpam-5494	314	18	tables	table	NOUN
ejpam-5494	314	19	1	1	NUM
ejpam-5494	314	20	and	and	CCONJ
ejpam-5494	314	21	2	2	NUM
ejpam-5494	314	22	deliver	deliver	VERB
ejpam-5494	314	23	a	a	DET
ejpam-5494	314	24	comparison	comparison	NOUN
ejpam-5494	314	25	of	of	ADP
ejpam-5494	314	26	numerical	numerical	ADJ
ejpam-5494	314	27	solutions	solution	NOUN
ejpam-5494	314	28	derived	derive	VERB
ejpam-5494	314	29	with	with	ADP
ejpam-5494	314	30	accurate	accurate	ADJ
ejpam-5494	314	31	solutions	solution	NOUN
ejpam-5494	314	32	.	.	PUNCT
ejpam-5494	315	1	furthermore	furthermore	ADV
ejpam-5494	315	2	,	,	PUNCT
ejpam-5494	315	3	an	an	DET
ejpam-5494	315	4	error	error	NOUN
ejpam-5494	315	5	analysis	analysis	NOUN
ejpam-5494	315	6	of	of	ADP
ejpam-5494	315	7	the	the	DET
ejpam-5494	315	8	sadik	sadik	PROPN
ejpam-5494	315	9	residual	residual	ADJ
ejpam-5494	315	10	power	power	NOUN
ejpam-5494	315	11	series	series	NOUN
ejpam-5494	315	12	method	method	NOUN
ejpam-5494	315	13	(	(	PUNCT
ejpam-5494	315	14	srpsm	srpsm	PROPN
ejpam-5494	315	15	)	)	PUNCT
ejpam-5494	315	16	and	and	CCONJ
ejpam-5494	315	17	the	the	DET
ejpam-5494	315	18	laplace	laplace	NOUN
ejpam-5494	315	19	residual	residual	ADJ
ejpam-5494	315	20	power	power	NOUN
ejpam-5494	315	21	series	series	PROPN
ejpam-5494	315	22	method	method	NOUN
ejpam-5494	315	23	(	(	PUNCT
ejpam-5494	315	24	lrpsm	lrpsm	PROPN
ejpam-5494	315	25	)	)	PUNCT
ejpam-5494	315	26	is	be	AUX
ejpam-5494	315	27	carried	carry	VERB
ejpam-5494	315	28	out	out	ADP
ejpam-5494	315	29	,	,	PUNCT
ejpam-5494	315	30	demonstrating	demonstrate	VERB
ejpam-5494	315	31	that	that	SCONJ
ejpam-5494	315	32	both	both	PRON
ejpam-5494	315	33	performed	perform	VERB
ejpam-5494	315	34	similarly	similarly	ADV
ejpam-5494	315	35	.	.	PUNCT
ejpam-5494	316	1	in	in	ADP
ejpam-5494	316	2	example	example	NOUN
ejpam-5494	316	3	2	2	NUM
ejpam-5494	316	4	,	,	PUNCT
ejpam-5494	316	5	the	the	DET
ejpam-5494	316	6	approximate	approximate	ADJ
ejpam-5494	316	7	solution	solution	NOUN
ejpam-5494	316	8	in	in	ADP
ejpam-5494	316	9	the	the	DET
ejpam-5494	316	10	form	form	NOUN
ejpam-5494	316	11	of	of	ADP
ejpam-5494	316	12	an	an	DET
ejpam-5494	316	13	infinite	infinite	ADJ
ejpam-5494	316	14	convergent	convergent	NOUN
ejpam-5494	316	15	series	series	NOUN
ejpam-5494	316	16	is	be	AUX
ejpam-5494	316	17	found	find	VERB
ejpam-5494	316	18	.	.	PUNCT
ejpam-5494	317	1	figure	figure	VERB
ejpam-5494	317	2	4	4	NUM
ejpam-5494	317	3	.	.	PUNCT
ejpam-5494	317	4	provides	provide	VERB
ejpam-5494	317	5	the	the	DET
ejpam-5494	317	6	outcome	outcome	NOUN
ejpam-5494	317	7	at	at	ADP
ejpam-5494	317	8	different	different	ADJ
ejpam-5494	317	9	values	value	NOUN
ejpam-5494	317	10	of	of	ADP
ejpam-5494	317	11	γ	γ	NOUN
ejpam-5494	317	12	when	when	SCONJ
ejpam-5494	317	13	x	x	PROPN
ejpam-5494	317	14	=	=	PUNCT
ejpam-5494	317	15	y	y	PROPN
ejpam-5494	317	16	=	=	PUNCT
ejpam-5494	317	17	0.2	0.2	NUM
ejpam-5494	317	18	and	and	CCONJ
ejpam-5494	317	19	the	the	DET
ejpam-5494	317	20	3d	3d	PROPN
ejpam-5494	317	21	p.	p.	NOUN
ejpam-5494	317	22	pue	pue	PROPN
ejpam-5494	317	23	-	-	PUNCT
ejpam-5494	317	24	on	on	ADP
ejpam-5494	317	25	/	/	SYM
ejpam-5494	317	26	eur	eur	NOUN
ejpam-5494	317	27	.	.	PUNCT
ejpam-5494	318	1	j.	j.	PROPN
ejpam-5494	318	2	pure	pure	PROPN
ejpam-5494	318	3	appl	appl	PROPN
ejpam-5494	318	4	.	.	PROPN
ejpam-5494	318	5	math	math	PROPN
ejpam-5494	318	6	,	,	PUNCT
ejpam-5494	318	7	17	17	NUM
ejpam-5494	318	8	(	(	PUNCT
ejpam-5494	318	9	4	4	NUM
ejpam-5494	318	10	)	)	PUNCT
ejpam-5494	318	11	(	(	PUNCT
ejpam-5494	318	12	2024	2024	NUM
ejpam-5494	318	13	)	)	PUNCT
ejpam-5494	318	14	,	,	PUNCT
ejpam-5494	318	15	3826	3826	NUM
ejpam-5494	318	16	-	-	SYM
ejpam-5494	318	17	3846	3846	NUM
ejpam-5494	318	18	3843	3843	NUM
ejpam-5494	318	19	figure	figure	NOUN
ejpam-5494	318	20	9	9	NUM
ejpam-5494	318	21	:	:	PUNCT
ejpam-5494	318	22	the	the	DET
ejpam-5494	318	23	graphics	graphic	NOUN
ejpam-5494	318	24	represent	represent	VERB
ejpam-5494	318	25	the	the	DET
ejpam-5494	318	26	approximate	approximate	ADJ
ejpam-5494	318	27	solution	solution	NOUN
ejpam-5494	318	28	w2(x	w2(x	PROPN
ejpam-5494	318	29	,	,	PUNCT
ejpam-5494	318	30	t	t	PROPN
ejpam-5494	318	31	)	)	PUNCT
ejpam-5494	318	32	with	with	ADP
ejpam-5494	318	33	different	different	ADJ
ejpam-5494	318	34	γ	γ	NOUN
ejpam-5494	318	35	values	value	NOUN
ejpam-5494	318	36	:	:	PUNCT
ejpam-5494	318	37	(	(	PUNCT
ejpam-5494	318	38	a	a	X
ejpam-5494	318	39	)	)	PUNCT
ejpam-5494	318	40	γ	γ	NOUN
ejpam-5494	318	41	=	=	SYM
ejpam-5494	318	42	0.4	0.4	NUM
ejpam-5494	318	43	,	,	PUNCT
ejpam-5494	318	44	(	(	PUNCT
ejpam-5494	318	45	b	b	X
ejpam-5494	318	46	)	)	PUNCT
ejpam-5494	318	47	γ	γ	NOUN
ejpam-5494	318	48	=	=	SYM
ejpam-5494	318	49	0.6	0.6	NUM
ejpam-5494	318	50	,	,	PUNCT
ejpam-5494	318	51	(	(	PUNCT
ejpam-5494	318	52	c	c	X
ejpam-5494	318	53	)	)	PUNCT
ejpam-5494	318	54	γ	γ	NOUN
ejpam-5494	318	55	=	=	NUM
ejpam-5494	318	56	0.8	0.8	NUM
ejpam-5494	318	57	,	,	PUNCT
ejpam-5494	318	58	and	and	CCONJ
ejpam-5494	318	59	(	(	PUNCT
ejpam-5494	318	60	d	d	X
ejpam-5494	318	61	)	)	PUNCT
ejpam-5494	318	62	γ	γ	NOUN
ejpam-5494	318	63	=	=	SYM
ejpam-5494	318	64	1.0	1.0	NUM
ejpam-5494	318	65	for	for	ADP
ejpam-5494	318	66	example	example	NOUN
ejpam-5494	318	67	3	3	NUM
ejpam-5494	318	68	.	.	X
ejpam-5494	318	69	graphic	graphic	NOUN
ejpam-5494	318	70	of	of	ADP
ejpam-5494	318	71	solutions	solution	NOUN
ejpam-5494	318	72	are	be	AUX
ejpam-5494	318	73	displayed	display	VERB
ejpam-5494	318	74	in	in	ADP
ejpam-5494	318	75	figures	figure	NOUN
ejpam-5494	318	76	5	5	NUM
ejpam-5494	318	77	and	and	CCONJ
ejpam-5494	318	78	6	6	NUM
ejpam-5494	318	79	.	.	PUNCT
ejpam-5494	319	1	moreover	moreover	ADV
ejpam-5494	319	2	,	,	PUNCT
ejpam-5494	319	3	the	the	DET
ejpam-5494	319	4	numerical	numerical	PROPN
ejpam-5494	319	5	simulation	simulation	NOUN
ejpam-5494	319	6	when	when	SCONJ
ejpam-5494	319	7	x	x	PROPN
ejpam-5494	319	8	=	=	SYM
ejpam-5494	319	9	y	y	NOUN
ejpam-5494	319	10	=	=	NUM
ejpam-5494	319	11	0.2	0.2	NUM
ejpam-5494	319	12	at	at	ADP
ejpam-5494	319	13	different	different	ADJ
ejpam-5494	319	14	values	value	NOUN
ejpam-5494	319	15	of	of	ADP
ejpam-5494	319	16	γ	γ	PROPN
ejpam-5494	319	17	is	be	AUX
ejpam-5494	319	18	shown	show	VERB
ejpam-5494	319	19	in	in	ADP
ejpam-5494	319	20	tables	table	NOUN
ejpam-5494	319	21	3	3	NUM
ejpam-5494	319	22	and	and	CCONJ
ejpam-5494	319	23	4	4	NUM
ejpam-5494	319	24	.	.	PUNCT
ejpam-5494	320	1	the	the	DET
ejpam-5494	320	2	sadik	sadik	PROPN
ejpam-5494	320	3	residual	residual	ADJ
ejpam-5494	320	4	power	power	NOUN
ejpam-5494	320	5	series	series	NOUN
ejpam-5494	320	6	method	method	NOUN
ejpam-5494	320	7	and	and	CCONJ
ejpam-5494	320	8	conformable	conformable	ADJ
ejpam-5494	320	9	residual	residual	ADJ
ejpam-5494	320	10	power	power	NOUN
ejpam-5494	320	11	series	series	NOUN
ejpam-5494	320	12	method	method	NOUN
ejpam-5494	320	13	(	(	PUNCT
ejpam-5494	320	14	crps	crps	PROPN
ejpam-5494	320	15	)	)	PUNCT
ejpam-5494	321	1	[	[	X
ejpam-5494	321	2	6	6	NUM
ejpam-5494	321	3	]	]	PUNCT
ejpam-5494	321	4	errors	error	NOUN
ejpam-5494	321	5	are	be	AUX
ejpam-5494	321	6	analyzed	analyze	VERB
ejpam-5494	321	7	at	at	ADP
ejpam-5494	321	8	the	the	DET
ejpam-5494	321	9	corresponding	corresponding	ADJ
ejpam-5494	321	10	points	point	NOUN
ejpam-5494	321	11	shown	show	VERB
ejpam-5494	321	12	in	in	ADP
ejpam-5494	321	13	tables	table	NOUN
ejpam-5494	321	14	5	5	NUM
ejpam-5494	321	15	and	and	CCONJ
ejpam-5494	321	16	6	6	NUM
ejpam-5494	321	17	.	.	PUNCT
ejpam-5494	322	1	this	this	PRON
ejpam-5494	322	2	demonstrates	demonstrate	VERB
ejpam-5494	322	3	that	that	SCONJ
ejpam-5494	322	4	both	both	PRON
ejpam-5494	322	5	have	have	VERB
ejpam-5494	322	6	equivalent	equivalent	ADJ
ejpam-5494	322	7	potential	potential	NOUN
ejpam-5494	322	8	.	.	PUNCT
ejpam-5494	323	1	in	in	ADP
ejpam-5494	323	2	example	example	NOUN
ejpam-5494	323	3	3	3	NUM
ejpam-5494	323	4	,	,	PUNCT
ejpam-5494	323	5	the	the	DET
ejpam-5494	323	6	graph	graph	NOUN
ejpam-5494	323	7	of	of	ADP
ejpam-5494	323	8	approximate	approximate	ADJ
ejpam-5494	323	9	solutions	solution	NOUN
ejpam-5494	323	10	at	at	ADP
ejpam-5494	323	11	different	different	ADJ
ejpam-5494	323	12	values	value	NOUN
ejpam-5494	323	13	of	of	ADP
ejpam-5494	323	14	γ	γ	NOUN
ejpam-5494	323	15	when	when	SCONJ
ejpam-5494	323	16	x	x	PROPN
ejpam-5494	323	17	=	=	SYM
ejpam-5494	323	18	0.5	0.5	NUM
ejpam-5494	323	19	are	be	AUX
ejpam-5494	323	20	indicated	indicate	VERB
ejpam-5494	323	21	in	in	ADP
ejpam-5494	323	22	figure	figure	NOUN
ejpam-5494	323	23	7	7	NUM
ejpam-5494	323	24	and	and	CCONJ
ejpam-5494	323	25	the	the	DET
ejpam-5494	323	26	3d	3d	PROPN
ejpam-5494	323	27	graphics	graphic	NOUN
ejpam-5494	323	28	of	of	ADP
ejpam-5494	323	29	approximate	approximate	ADJ
ejpam-5494	323	30	solutions	solution	NOUN
ejpam-5494	323	31	are	be	AUX
ejpam-5494	323	32	manifested	manifest	VERB
ejpam-5494	323	33	in	in	ADP
ejpam-5494	323	34	figures	figure	NOUN
ejpam-5494	323	35	8	8	NUM
ejpam-5494	323	36	and	and	CCONJ
ejpam-5494	323	37	9	9	NUM
ejpam-5494	323	38	.	.	PUNCT
ejpam-5494	324	1	in	in	ADP
ejpam-5494	324	2	addition	addition	NOUN
ejpam-5494	324	3	,	,	PUNCT
ejpam-5494	324	4	tables	table	NOUN
ejpam-5494	324	5	7	7	NUM
ejpam-5494	324	6	and	and	CCONJ
ejpam-5494	324	7	8	8	NUM
ejpam-5494	324	8	present	present	VERB
ejpam-5494	324	9	the	the	DET
ejpam-5494	324	10	numerical	numerical	ADJ
ejpam-5494	324	11	solution	solution	NOUN
ejpam-5494	324	12	at	at	ADP
ejpam-5494	324	13	different	different	ADJ
ejpam-5494	324	14	values	value	NOUN
ejpam-5494	324	15	of	of	ADP
ejpam-5494	324	16	γ	γ	PROPN
ejpam-5494	324	17	.	.	PROPN
ejpam-5494	324	18	5	5	NUM
ejpam-5494	324	19	.	.	X
ejpam-5494	324	20	conclusion	conclusion	NOUN
ejpam-5494	324	21	this	this	DET
ejpam-5494	324	22	investigation	investigation	NOUN
ejpam-5494	324	23	successfully	successfully	ADV
ejpam-5494	324	24	addressed	address	VERB
ejpam-5494	324	25	the	the	DET
ejpam-5494	324	26	system	system	NOUN
ejpam-5494	324	27	of	of	ADP
ejpam-5494	324	28	nonlinear	nonlinear	ADJ
ejpam-5494	324	29	fractional	fractional	ADJ
ejpam-5494	324	30	partial	partial	ADJ
ejpam-5494	324	31	differential	differential	NOUN
ejpam-5494	324	32	equations	equation	NOUN
ejpam-5494	324	33	by	by	ADP
ejpam-5494	324	34	using	use	VERB
ejpam-5494	324	35	the	the	DET
ejpam-5494	324	36	sadik	sadik	PROPN
ejpam-5494	324	37	residual	residual	ADJ
ejpam-5494	324	38	power	power	NOUN
ejpam-5494	324	39	series	series	NOUN
ejpam-5494	324	40	method	method	NOUN
ejpam-5494	324	41	.	.	PUNCT
ejpam-5494	325	1	the	the	DET
ejpam-5494	325	2	employed	employ	VERB
ejpam-5494	325	3	methodology	methodology	NOUN
ejpam-5494	325	4	offers	offer	VERB
ejpam-5494	325	5	a	a	DET
ejpam-5494	325	6	solution	solution	NOUN
ejpam-5494	325	7	to	to	ADP
ejpam-5494	325	8	the	the	DET
ejpam-5494	325	9	nonlinear	nonlinear	ADJ
ejpam-5494	325	10	problem	problem	NOUN
ejpam-5494	325	11	without	without	ADP
ejpam-5494	325	12	necessitating	necessitate	VERB
ejpam-5494	325	13	the	the	DET
ejpam-5494	325	14	utilization	utilization	NOUN
ejpam-5494	325	15	of	of	ADP
ejpam-5494	325	16	adomian	adomian	NOUN
ejpam-5494	325	17	polynomials	polynomial	NOUN
ejpam-5494	325	18	,	,	PUNCT
ejpam-5494	325	19	linearization	linearization	NOUN
ejpam-5494	325	20	techniques	technique	NOUN
ejpam-5494	325	21	,	,	PUNCT
ejpam-5494	325	22	or	or	CCONJ
ejpam-5494	325	23	perturbation	perturbation	NOUN
ejpam-5494	325	24	processes	process	NOUN
ejpam-5494	325	25	.	.	PUNCT
ejpam-5494	326	1	the	the	DET
ejpam-5494	326	2	ease	ease	NOUN
ejpam-5494	326	3	of	of	ADP
ejpam-5494	326	4	use	use	NOUN
ejpam-5494	326	5	of	of	ADP
ejpam-5494	326	6	the	the	DET
ejpam-5494	326	7	technique	technique	NOUN
ejpam-5494	326	8	due	due	ADP
ejpam-5494	326	9	to	to	ADP
ejpam-5494	326	10	condition	condition	NOUN
ejpam-5494	326	11	(	(	PUNCT
ejpam-5494	326	12	9	9	NUM
ejpam-5494	326	13	)	)	PUNCT
ejpam-5494	326	14	is	be	AUX
ejpam-5494	326	15	an	an	DET
ejpam-5494	326	16	advantage	advantage	NOUN
ejpam-5494	326	17	compared	compare	VERB
ejpam-5494	326	18	to	to	ADP
ejpam-5494	326	19	traditional	traditional	ADJ
ejpam-5494	326	20	power	power	NOUN
ejpam-5494	326	21	series	series	NOUN
ejpam-5494	326	22	approaches	approach	NOUN
ejpam-5494	326	23	,	,	PUNCT
ejpam-5494	326	24	which	which	PRON
ejpam-5494	326	25	involve	involve	VERB
ejpam-5494	326	26	differentiation	differentiation	NOUN
ejpam-5494	326	27	to	to	PART
ejpam-5494	326	28	obtain	obtain	VERB
ejpam-5494	326	29	the	the	DET
ejpam-5494	326	30	series	series	NOUN
ejpam-5494	326	31	solution	solution	NOUN
ejpam-5494	326	32	coefficients	coefficient	NOUN
ejpam-5494	326	33	.	.	PUNCT
ejpam-5494	327	1	therefore	therefore	ADV
ejpam-5494	327	2	,	,	PUNCT
ejpam-5494	327	3	the	the	DET
ejpam-5494	327	4	recommended	recommend	VERB
ejpam-5494	327	5	approach	approach	NOUN
ejpam-5494	327	6	requires	require	VERB
ejpam-5494	327	7	less	less	ADJ
ejpam-5494	327	8	time	time	NOUN
ejpam-5494	327	9	for	for	ADP
ejpam-5494	327	10	computation	computation	NOUN
ejpam-5494	327	11	.	.	PUNCT
ejpam-5494	328	1	the	the	DET
ejpam-5494	328	2	references	reference	NOUN
ejpam-5494	328	3	3844	3844	NUM
ejpam-5494	328	4	obtained	obtain	VERB
ejpam-5494	328	5	results	result	NOUN
ejpam-5494	328	6	are	be	AUX
ejpam-5494	328	7	expressed	express	VERB
ejpam-5494	328	8	as	as	ADP
ejpam-5494	328	9	a	a	DET
ejpam-5494	328	10	power	power	NOUN
ejpam-5494	328	11	series	series	NOUN
ejpam-5494	328	12	that	that	PRON
ejpam-5494	328	13	converges	converge	VERB
ejpam-5494	328	14	to	to	ADP
ejpam-5494	328	15	the	the	DET
ejpam-5494	328	16	closed	closed	ADJ
ejpam-5494	328	17	form	form	NOUN
ejpam-5494	328	18	via	via	ADP
ejpam-5494	328	19	mittag	mittag	ADJ
ejpam-5494	328	20	-	-	PUNCT
ejpam-5494	328	21	leffler	leffler	NOUN
ejpam-5494	328	22	functions	function	NOUN
ejpam-5494	328	23	,	,	PUNCT
ejpam-5494	328	24	as	as	SCONJ
ejpam-5494	328	25	shown	show	VERB
ejpam-5494	328	26	in	in	ADP
ejpam-5494	328	27	example	example	NOUN
ejpam-5494	328	28	1	1	NUM
ejpam-5494	328	29	and	and	CCONJ
ejpam-5494	328	30	example	example	NOUN
ejpam-5494	328	31	2	2	NUM
ejpam-5494	328	32	,	,	PUNCT
ejpam-5494	328	33	while	while	SCONJ
ejpam-5494	328	34	in	in	ADP
ejpam-5494	328	35	example	example	NOUN
ejpam-5494	328	36	3	3	NUM
ejpam-5494	328	37	,	,	PUNCT
ejpam-5494	328	38	the	the	DET
ejpam-5494	328	39	outcome	outcome	NOUN
ejpam-5494	328	40	is	be	AUX
ejpam-5494	328	41	written	write	VERB
ejpam-5494	328	42	in	in	ADP
ejpam-5494	328	43	the	the	DET
ejpam-5494	328	44	form	form	NOUN
ejpam-5494	328	45	of	of	ADP
ejpam-5494	328	46	a	a	DET
ejpam-5494	328	47	truncated	truncated	ADJ
ejpam-5494	328	48	power	power	NOUN
ejpam-5494	328	49	series	series	PROPN
ejpam-5494	328	50	.	.	PUNCT
ejpam-5494	329	1	numerical	numerical	PROPN
ejpam-5494	329	2	simulation	simulation	PROPN
ejpam-5494	329	3	results	result	NOUN
ejpam-5494	329	4	and	and	CCONJ
ejpam-5494	329	5	3d	3d	NUM
ejpam-5494	329	6	graphics	graphic	NOUN
ejpam-5494	329	7	confirm	confirm	VERB
ejpam-5494	329	8	that	that	SCONJ
ejpam-5494	329	9	the	the	DET
ejpam-5494	329	10	method	method	NOUN
ejpam-5494	329	11	is	be	AUX
ejpam-5494	329	12	an	an	DET
ejpam-5494	329	13	efficient	efficient	ADJ
ejpam-5494	329	14	,	,	PUNCT
ejpam-5494	329	15	reliable	reliable	ADJ
ejpam-5494	329	16	,	,	PUNCT
ejpam-5494	329	17	and	and	CCONJ
ejpam-5494	329	18	accurate	accurate	ADJ
ejpam-5494	329	19	method	method	NOUN
ejpam-5494	329	20	for	for	ADP
ejpam-5494	329	21	solving	solve	VERB
ejpam-5494	329	22	non	non	ADJ
ejpam-5494	329	23	-	-	ADJ
ejpam-5494	329	24	linear	linear	ADJ
ejpam-5494	329	25	problems	problem	NOUN
ejpam-5494	329	26	.	.	PUNCT
ejpam-5494	330	1	based	base	VERB
ejpam-5494	330	2	on	on	ADP
ejpam-5494	330	3	the	the	DET
ejpam-5494	330	4	information	information	NOUN
ejpam-5494	330	5	above	above	ADV
ejpam-5494	330	6	,	,	PUNCT
ejpam-5494	330	7	the	the	DET
ejpam-5494	330	8	sadik	sadik	PROPN
ejpam-5494	330	9	residual	residual	ADJ
ejpam-5494	330	10	power	power	NOUN
ejpam-5494	330	11	series	series	PROPN
ejpam-5494	330	12	approach	approach	NOUN
ejpam-5494	330	13	is	be	AUX
ejpam-5494	330	14	an	an	DET
ejpam-5494	330	15	efficient	efficient	ADJ
ejpam-5494	330	16	,	,	PUNCT
ejpam-5494	330	17	dependable	dependable	ADJ
ejpam-5494	330	18	,	,	PUNCT
ejpam-5494	330	19	and	and	CCONJ
ejpam-5494	330	20	practical	practical	ADJ
ejpam-5494	330	21	method	method	NOUN
ejpam-5494	330	22	for	for	ADP
ejpam-5494	330	23	solving	solve	VERB
ejpam-5494	330	24	nonlinear	nonlinear	ADJ
ejpam-5494	330	25	fractional	fractional	ADJ
ejpam-5494	330	26	order	order	NOUN
ejpam-5494	330	27	partial	partial	ADJ
ejpam-5494	330	28	differential	differential	NOUN
ejpam-5494	330	29	equation	equation	NOUN
ejpam-5494	330	30	systems	system	NOUN
ejpam-5494	330	31	.	.	PUNCT
ejpam-5494	331	1	it	it	PRON
ejpam-5494	331	2	is	be	AUX
ejpam-5494	331	3	suitable	suitable	ADJ
ejpam-5494	331	4	for	for	ADP
ejpam-5494	331	5	tackling	tackle	VERB
ejpam-5494	331	6	other	other	ADJ
ejpam-5494	331	7	types	type	NOUN
ejpam-5494	331	8	of	of	ADP
ejpam-5494	331	9	non	non	ADJ
ejpam-5494	331	10	-	-	ADJ
ejpam-5494	331	11	linear	linear	ADJ
ejpam-5494	331	12	fractional	fractional	ADJ
ejpam-5494	331	13	calculus	calculus	NOUN
ejpam-5494	331	14	issues	issue	NOUN
ejpam-5494	331	15	.	.	PUNCT
ejpam-5494	332	1	acknowledgements	acknowledgement	NOUN
ejpam-5494	332	2	this	this	DET
ejpam-5494	332	3	research	research	NOUN
ejpam-5494	332	4	project	project	NOUN
ejpam-5494	332	5	was	be	AUX
ejpam-5494	332	6	financially	financially	ADV
ejpam-5494	332	7	supported	support	VERB
ejpam-5494	332	8	by	by	ADP
ejpam-5494	332	9	thailand	thailand	PROPN
ejpam-5494	332	10	science	science	PROPN
ejpam-5494	332	11	research	research	PROPN
ejpam-5494	332	12	and	and	CCONJ
ejpam-5494	332	13	innovation	innovation	NOUN
ejpam-5494	332	14	(	(	PUNCT
ejpam-5494	332	15	tsri	tsri	PROPN
ejpam-5494	332	16	)	)	PUNCT
ejpam-5494	332	17	.	.	PUNCT
ejpam-5494	333	1	the	the	DET
ejpam-5494	333	2	author	author	NOUN
ejpam-5494	333	3	is	be	AUX
ejpam-5494	333	4	grateful	grateful	ADJ
ejpam-5494	333	5	to	to	ADP
ejpam-5494	333	6	the	the	DET
ejpam-5494	333	7	reviewers	reviewer	NOUN
ejpam-5494	333	8	for	for	ADP
ejpam-5494	333	9	their	their	PRON
ejpam-5494	333	10	informative	informative	ADJ
ejpam-5494	333	11	suggestions	suggestion	NOUN
ejpam-5494	333	12	and	and	CCONJ
ejpam-5494	333	13	feedback	feedback	NOUN
ejpam-5494	333	14	.	.	PUNCT
ejpam-5494	334	1	references	reference	NOUN
ejpam-5494	334	2	[	[	X
ejpam-5494	334	3	1	1	NUM
ejpam-5494	334	4	]	]	X
ejpam-5494	334	5	o.	o.	PROPN
ejpam-5494	334	6	abdulaziz	abdulaziz	PROPN
ejpam-5494	334	7	,	,	PUNCT
ejpam-5494	334	8	i.	i.	PROPN
ejpam-5494	334	9	hashim	hashim	PROPN
ejpam-5494	334	10	,	,	PUNCT
ejpam-5494	334	11	and	and	CCONJ
ejpam-5494	334	12	s.	s.	PROPN
ejpam-5494	334	13	momani	momani	PROPN
ejpam-5494	334	14	.	.	PUNCT
ejpam-5494	335	1	solving	solve	VERB
ejpam-5494	335	2	systems	system	NOUN
ejpam-5494	335	3	of	of	ADP
ejpam-5494	335	4	fractional	fractional	ADJ
ejpam-5494	335	5	differential	differential	ADJ
ejpam-5494	335	6	equations	equation	NOUN
ejpam-5494	335	7	by	by	ADP
ejpam-5494	335	8	homotopy	homotopy	NOUN
ejpam-5494	335	9	-	-	PUNCT
ejpam-5494	335	10	perturbation	perturbation	NOUN
ejpam-5494	335	11	method	method	NOUN
ejpam-5494	335	12	.	.	PUNCT
ejpam-5494	336	1	physics	physics	NOUN
ejpam-5494	336	2	letters	letter	NOUN
ejpam-5494	336	3	a	a	PRON
ejpam-5494	336	4	,	,	PUNCT
ejpam-5494	336	5	372(4):451–459	372(4):451–459	NUM
ejpam-5494	336	6	,	,	PUNCT
ejpam-5494	336	7	2008	2008	NUM
ejpam-5494	336	8	.	.	PUNCT
ejpam-5494	337	1	[	[	X
ejpam-5494	337	2	2	2	NUM
ejpam-5494	337	3	]	]	PUNCT
ejpam-5494	337	4	a.	a.	NOUN
ejpam-5494	337	5	t.	t.	PROPN
ejpam-5494	337	6	alabdala	alabdala	PROPN
ejpam-5494	337	7	,	,	PUNCT
ejpam-5494	337	8	b.	b.	PROPN
ejpam-5494	337	9	n.	n.	PROPN
ejpam-5494	337	10	abood	abood	PROPN
ejpam-5494	337	11	,	,	PUNCT
ejpam-5494	337	12	s.	s.	PROPN
ejpam-5494	337	13	s.	s.	PROPN
ejpam-5494	337	14	redhwan	redhwan	PROPN
ejpam-5494	337	15	,	,	PUNCT
ejpam-5494	337	16	and	and	CCONJ
ejpam-5494	337	17	s.	s.	PROPN
ejpam-5494	337	18	alkhatib	alkhatib	PROPN
ejpam-5494	337	19	.	.	PUNCT
ejpam-5494	338	1	caputo	caputo	PROPN
ejpam-5494	338	2	delayed	delay	VERB
ejpam-5494	338	3	fractional	fractional	ADJ
ejpam-5494	338	4	differential	differential	ADJ
ejpam-5494	338	5	equations	equation	NOUN
ejpam-5494	338	6	by	by	ADP
ejpam-5494	338	7	sadik	sadik	PROPN
ejpam-5494	338	8	transform	transform	PROPN
ejpam-5494	338	9	.	.	PUNCT
ejpam-5494	339	1	nonlinear	nonlinear	ADJ
ejpam-5494	339	2	functional	functional	ADJ
ejpam-5494	339	3	analysis	analysis	NOUN
ejpam-5494	339	4	and	and	CCONJ
ejpam-5494	339	5	applications	application	NOUN
ejpam-5494	339	6	,	,	PUNCT
ejpam-5494	339	7	28(2):439–448	28(2):439–448	NUM
ejpam-5494	339	8	,	,	PUNCT
ejpam-5494	339	9	2023	2023	NUM
ejpam-5494	339	10	.	.	PUNCT
ejpam-5494	340	1	[	[	X
ejpam-5494	340	2	3	3	NUM
ejpam-5494	340	3	]	]	PUNCT
ejpam-5494	340	4	m.	m.	NOUN
ejpam-5494	340	5	alaroud	alaroud	PROPN
ejpam-5494	340	6	.	.	PUNCT
ejpam-5494	341	1	application	application	NOUN
ejpam-5494	341	2	of	of	ADP
ejpam-5494	341	3	laplace	laplace	NOUN
ejpam-5494	341	4	residual	residual	ADJ
ejpam-5494	341	5	power	power	NOUN
ejpam-5494	341	6	series	series	PROPN
ejpam-5494	341	7	method	method	NOUN
ejpam-5494	341	8	for	for	ADP
ejpam-5494	341	9	approximate	approximate	ADJ
ejpam-5494	341	10	solutions	solution	NOUN
ejpam-5494	341	11	of	of	ADP
ejpam-5494	341	12	fractional	fractional	ADJ
ejpam-5494	341	13	ivp	ivp	PROPN
ejpam-5494	341	14	’s	’s	NOUN
ejpam-5494	341	15	.	.	PUNCT
ejpam-5494	342	1	alexandria	alexandria	PROPN
ejpam-5494	342	2	engineering	engineering	PROPN
ejpam-5494	342	3	journal	journal	PROPN
ejpam-5494	342	4	,	,	PUNCT
ejpam-5494	342	5	61(2	61(2	NUM
ejpam-5494	342	6	)	)	PUNCT
ejpam-5494	342	7	,	,	PUNCT
ejpam-5494	342	8	2022	2022	NUM
ejpam-5494	342	9	.	.	PUNCT
ejpam-5494	343	1	[	[	X
ejpam-5494	343	2	4	4	NUM
ejpam-5494	343	3	]	]	PUNCT
ejpam-5494	343	4	a.	a.	NOUN
ejpam-5494	343	5	a.	a.	PROPN
ejpam-5494	343	6	alderremy	alderremy	PROPN
ejpam-5494	343	7	,	,	PUNCT
ejpam-5494	343	8	r.	r.	PROPN
ejpam-5494	343	9	shah	shah	PROPN
ejpam-5494	343	10	,	,	PUNCT
ejpam-5494	343	11	n.	n.	PROPN
ejpam-5494	343	12	iqbal	iqbal	PROPN
ejpam-5494	343	13	,	,	PUNCT
ejpam-5494	343	14	s.	s.	PROPN
ejpam-5494	343	15	aly	aly	PROPN
ejpam-5494	343	16	,	,	PUNCT
ejpam-5494	343	17	and	and	CCONJ
ejpam-5494	343	18	k.	k.	PROPN
ejpam-5494	343	19	nonlaopon	nonlaopon	PROPN
ejpam-5494	343	20	.	.	PUNCT
ejpam-5494	344	1	fractional	fractional	ADJ
ejpam-5494	344	2	series	series	PROPN
ejpam-5494	344	3	solution	solution	NOUN
ejpam-5494	344	4	construction	construction	NOUN
ejpam-5494	344	5	for	for	ADP
ejpam-5494	344	6	nonlinear	nonlinear	ADJ
ejpam-5494	344	7	fractional	fractional	ADJ
ejpam-5494	344	8	reaction	reaction	NOUN
ejpam-5494	344	9	-	-	PUNCT
ejpam-5494	344	10	diffusion	diffusion	NOUN
ejpam-5494	344	11	brusselator	brusselator	NOUN
ejpam-5494	344	12	model	model	NOUN
ejpam-5494	344	13	utilizing	utilize	VERB
ejpam-5494	344	14	laplace	laplace	NOUN
ejpam-5494	344	15	residual	residual	ADJ
ejpam-5494	344	16	power	power	NOUN
ejpam-5494	344	17	series	series	PROPN
ejpam-5494	344	18	.	.	PUNCT
ejpam-5494	345	1	symmetry	symmetry	PROPN
ejpam-5494	345	2	,	,	PUNCT
ejpam-5494	345	3	14(1944	14(1944	NUM
ejpam-5494	345	4	)	)	PUNCT
ejpam-5494	345	5	,	,	PUNCT
ejpam-5494	345	6	2022	2022	NUM
ejpam-5494	345	7	.	.	PUNCT
ejpam-5494	346	1	[	[	X
ejpam-5494	346	2	5	5	NUM
ejpam-5494	346	3	]	]	PUNCT
ejpam-5494	346	4	a.	a.	NOUN
ejpam-5494	346	5	s.	s.	PROPN
ejpam-5494	346	6	alshehry	alshehry	PROPN
ejpam-5494	346	7	,	,	PUNCT
ejpam-5494	346	8	r.	r.	PROPN
ejpam-5494	346	9	ullah	ullah	PROPN
ejpam-5494	346	10	,	,	PUNCT
ejpam-5494	346	11	n.	n.	PROPN
ejpam-5494	346	12	a.	a.	NOUN
ejpam-5494	346	13	shah	shah	PROPN
ejpam-5494	346	14	,	,	PUNCT
ejpam-5494	346	15	r.	r.	PROPN
ejpam-5494	346	16	shah	shah	PROPN
ejpam-5494	346	17	,	,	PUNCT
ejpam-5494	346	18	and	and	CCONJ
ejpam-5494	346	19	k.	k.	PROPN
ejpam-5494	346	20	nonlaopon	nonlaopon	PROPN
ejpam-5494	346	21	.	.	PUNCT
ejpam-5494	347	1	implementation	implementation	NOUN
ejpam-5494	347	2	of	of	ADP
ejpam-5494	347	3	yang	yang	PROPN
ejpam-5494	347	4	residual	residual	ADJ
ejpam-5494	347	5	power	power	NOUN
ejpam-5494	347	6	series	series	PROPN
ejpam-5494	347	7	method	method	NOUN
ejpam-5494	347	8	to	to	PART
ejpam-5494	347	9	solve	solve	VERB
ejpam-5494	347	10	fractional	fractional	ADJ
ejpam-5494	347	11	non	non	ADJ
ejpam-5494	347	12	-	-	ADJ
ejpam-5494	347	13	linear	linear	ADJ
ejpam-5494	347	14	systems	system	NOUN
ejpam-5494	347	15	.	.	PUNCT
ejpam-5494	348	1	aims	aim	VERB
ejpam-5494	348	2	mathematics	mathematic	NOUN
ejpam-5494	348	3	,	,	PUNCT
ejpam-5494	348	4	8(4):8294–8309	8(4):8294–8309	NUM
ejpam-5494	348	5	,	,	PUNCT
ejpam-5494	348	6	2023	2023	NUM
ejpam-5494	348	7	.	.	PUNCT
ejpam-5494	349	1	[	[	X
ejpam-5494	349	2	6	6	NUM
ejpam-5494	349	3	]	]	PUNCT
ejpam-5494	349	4	a.	a.	NOUN
ejpam-5494	349	5	arafa	arafa	PROPN
ejpam-5494	349	6	.	.	PUNCT
ejpam-5494	350	1	a	a	DET
ejpam-5494	350	2	different	different	ADJ
ejpam-5494	350	3	approach	approach	NOUN
ejpam-5494	350	4	for	for	ADP
ejpam-5494	350	5	conformable	conformable	ADJ
ejpam-5494	350	6	fractional	fractional	ADJ
ejpam-5494	350	7	biochemical	biochemical	ADJ
ejpam-5494	350	8	reactiondiffusion	reactiondiffusion	NOUN
ejpam-5494	350	9	models	model	NOUN
ejpam-5494	350	10	.	.	PUNCT
ejpam-5494	351	1	applied	apply	VERB
ejpam-5494	351	2	mathematics	mathematic	NOUN
ejpam-5494	351	3	-	-	PUNCT
ejpam-5494	351	4	a	a	DET
ejpam-5494	351	5	journal	journal	NOUN
ejpam-5494	351	6	chinese	chinese	ADJ
ejpam-5494	351	7	universities	university	NOUN
ejpam-5494	351	8	.	.	PUNCT
ejpam-5494	351	9	,	,	PUNCT
ejpam-5494	351	10	35:452–467	35:452–467	NUM
ejpam-5494	351	11	,	,	PUNCT
ejpam-5494	351	12	2020	2020	NUM
ejpam-5494	351	13	.	.	PUNCT
ejpam-5494	352	1	[	[	X
ejpam-5494	352	2	7	7	X
ejpam-5494	352	3	]	]	X
ejpam-5494	352	4	m.	m.	PROPN
ejpam-5494	352	5	caputo	caputo	PROPN
ejpam-5494	352	6	.	.	PUNCT
ejpam-5494	352	7	linear	linear	PROPN
ejpam-5494	352	8	models	model	NOUN
ejpam-5494	352	9	of	of	ADP
ejpam-5494	352	10	dissipation	dissipation	NOUN
ejpam-5494	352	11	whose	whose	DET
ejpam-5494	352	12	q	q	NOUN
ejpam-5494	352	13	is	be	AUX
ejpam-5494	352	14	almost	almost	ADV
ejpam-5494	352	15	frequency	frequency	ADJ
ejpam-5494	352	16	independent	independent	ADJ
ejpam-5494	352	17	.	.	PUNCT
ejpam-5494	353	1	part	part	PROPN
ejpam-5494	353	2	ii	ii	PROPN
ejpam-5494	353	3	.	.	PROPN
ejpam-5494	353	4	geophysical	geophysical	ADJ
ejpam-5494	353	5	journal	journal	NOUN
ejpam-5494	353	6	of	of	ADP
ejpam-5494	353	7	the	the	DET
ejpam-5494	353	8	royal	royal	ADJ
ejpam-5494	353	9	astronomical	astronomical	ADJ
ejpam-5494	353	10	society	society	NOUN
ejpam-5494	353	11	,	,	PUNCT
ejpam-5494	353	12	13:529–539	13:529–539	PROPN
ejpam-5494	353	13	,	,	PUNCT
ejpam-5494	353	14	1967	1967	NUM
ejpam-5494	353	15	.	.	PUNCT
ejpam-5494	354	1	references	reference	NOUN
ejpam-5494	354	2	3845	3845	NUM
ejpam-5494	355	1	[	[	X
ejpam-5494	355	2	8	8	NUM
ejpam-5494	355	3	]	]	PUNCT
ejpam-5494	355	4	j.	j.	PROPN
ejpam-5494	355	5	p.	p.	PROPN
ejpam-5494	355	6	chauhan	chauhan	PROPN
ejpam-5494	355	7	and	and	CCONJ
ejpam-5494	355	8	s.	s.	PROPN
ejpam-5494	355	9	r.	r.	PROPN
ejpam-5494	355	10	khirsariya	khirsariya	PROPN
ejpam-5494	355	11	.	.	PUNCT
ejpam-5494	356	1	a	a	DET
ejpam-5494	356	2	semi	semi	ADJ
ejpam-5494	356	3	-	-	ADJ
ejpam-5494	356	4	analytic	analytic	ADJ
ejpam-5494	356	5	method	method	NOUN
ejpam-5494	356	6	to	to	PART
ejpam-5494	356	7	solve	solve	VERB
ejpam-5494	356	8	nonlinear	nonlinear	ADJ
ejpam-5494	356	9	differential	differential	ADJ
ejpam-5494	356	10	equations	equation	NOUN
ejpam-5494	356	11	with	with	ADP
ejpam-5494	356	12	arbitrary	arbitrary	ADJ
ejpam-5494	356	13	order	order	NOUN
ejpam-5494	356	14	.	.	PUNCT
ejpam-5494	357	1	results	result	NOUN
ejpam-5494	357	2	in	in	ADP
ejpam-5494	357	3	control	control	NOUN
ejpam-5494	357	4	and	and	CCONJ
ejpam-5494	357	5	optimization	optimization	NOUN
ejpam-5494	357	6	,	,	PUNCT
ejpam-5494	357	7	12(100267	12(100267	NUM
ejpam-5494	357	8	)	)	PUNCT
ejpam-5494	357	9	,	,	PUNCT
ejpam-5494	357	10	2023	2023	NUM
ejpam-5494	357	11	.	.	PUNCT
ejpam-5494	358	1	[	[	X
ejpam-5494	358	2	9	9	NUM
ejpam-5494	358	3	]	]	PUNCT
ejpam-5494	358	4	m.	m.	NOUN
ejpam-5494	358	5	derakhshan	derakhshan	PROPN
ejpam-5494	358	6	.	.	PUNCT
ejpam-5494	359	1	analytical	analytical	ADJ
ejpam-5494	359	2	solutions	solution	NOUN
ejpam-5494	359	3	for	for	ADP
ejpam-5494	359	4	the	the	DET
ejpam-5494	359	5	equal	equal	ADJ
ejpam-5494	359	6	width	width	ADJ
ejpam-5494	359	7	equations	equation	NOUN
ejpam-5494	359	8	containing	contain	VERB
ejpam-5494	359	9	generalized	generalize	VERB
ejpam-5494	359	10	fractional	fractional	ADJ
ejpam-5494	359	11	derivative	derivative	NOUN
ejpam-5494	359	12	using	use	VERB
ejpam-5494	359	13	the	the	DET
ejpam-5494	359	14	efficient	efficient	ADJ
ejpam-5494	359	15	combined	combine	VERB
ejpam-5494	359	16	method	method	NOUN
ejpam-5494	359	17	.	.	PUNCT
ejpam-5494	360	1	international	international	ADJ
ejpam-5494	360	2	journal	journal	PROPN
ejpam-5494	360	3	of	of	ADP
ejpam-5494	360	4	differential	differential	ADJ
ejpam-5494	360	5	equations	equation	NOUN
ejpam-5494	360	6	,	,	PUNCT
ejpam-5494	360	7	2021(7066398):14	2021(7066398):14	NUM
ejpam-5494	360	8	pages	page	NOUN
ejpam-5494	360	9	,	,	PUNCT
ejpam-5494	360	10	2021	2021	NUM
ejpam-5494	360	11	.	.	PUNCT
ejpam-5494	361	1	[	[	X
ejpam-5494	361	2	10	10	NUM
ejpam-5494	361	3	]	]	X
ejpam-5494	361	4	a.	a.	PROPN
ejpam-5494	361	5	el	el	PROPN
ejpam-5494	361	6	-	-	PUNCT
ejpam-5494	361	7	ajou	ajou	ADJ
ejpam-5494	361	8	,	,	PUNCT
ejpam-5494	361	9	o.	o.	NOUN
ejpam-5494	361	10	a.	a.	NOUN
ejpam-5494	361	11	arqub	arqub	NOUN
ejpam-5494	361	12	,	,	PUNCT
ejpam-5494	361	13	and	and	CCONJ
ejpam-5494	361	14	s.	s.	PROPN
ejpam-5494	361	15	momani	momani	PROPN
ejpam-5494	361	16	.	.	PUNCT
ejpam-5494	362	1	approximate	approximate	ADJ
ejpam-5494	362	2	analytical	analytical	ADJ
ejpam-5494	362	3	solution	solution	NOUN
ejpam-5494	362	4	of	of	ADP
ejpam-5494	362	5	the	the	DET
ejpam-5494	362	6	nonlinear	nonlinear	ADJ
ejpam-5494	362	7	fractional	fractional	ADJ
ejpam-5494	362	8	kdv	kdv	NOUN
ejpam-5494	362	9	-	-	PUNCT
ejpam-5494	362	10	burgers	burger	NOUN
ejpam-5494	362	11	equation	equation	NOUN
ejpam-5494	362	12	:	:	PUNCT
ejpam-5494	362	13	a	a	DET
ejpam-5494	362	14	new	new	ADJ
ejpam-5494	362	15	iterative	iterative	NOUN
ejpam-5494	362	16	algorithm	algorithm	NOUN
ejpam-5494	362	17	.	.	PUNCT
ejpam-5494	363	1	journal	journal	NOUN
ejpam-5494	363	2	of	of	ADP
ejpam-5494	363	3	computational	computational	ADJ
ejpam-5494	363	4	physics	physics	NOUN
ejpam-5494	363	5	.	.	PUNCT
ejpam-5494	363	6	,	,	PUNCT
ejpam-5494	364	1	293:81–95	293:81–95	NUM
ejpam-5494	364	2	,	,	PUNCT
ejpam-5494	364	3	2015	2015	NUM
ejpam-5494	364	4	.	.	PUNCT
ejpam-5494	365	1	[	[	X
ejpam-5494	365	2	11	11	NUM
ejpam-5494	365	3	]	]	X
ejpam-5494	365	4	a.	a.	PROPN
ejpam-5494	365	5	el	el	PROPN
ejpam-5494	365	6	-	-	PUNCT
ejpam-5494	365	7	ajou	ajou	ADJ
ejpam-5494	365	8	,	,	PUNCT
ejpam-5494	365	9	o.	o.	NOUN
ejpam-5494	365	10	a.	a.	NOUN
ejpam-5494	365	11	arqub	arqub	PROPN
ejpam-5494	365	12	,	,	PUNCT
ejpam-5494	365	13	z.	z.	PROPN
ejpam-5494	365	14	a.	a.	NOUN
ejpam-5494	365	15	zhour	zhour	PROPN
ejpam-5494	365	16	,	,	PUNCT
ejpam-5494	365	17	and	and	CCONJ
ejpam-5494	365	18	s.	s.	PROPN
ejpam-5494	365	19	momani	momani	PROPN
ejpam-5494	365	20	.	.	PUNCT
ejpam-5494	366	1	new	new	ADJ
ejpam-5494	366	2	results	result	NOUN
ejpam-5494	366	3	on	on	ADP
ejpam-5494	366	4	fractional	fractional	ADJ
ejpam-5494	366	5	power	power	NOUN
ejpam-5494	366	6	series	series	NOUN
ejpam-5494	366	7	:	:	PUNCT
ejpam-5494	366	8	theories	theory	NOUN
ejpam-5494	366	9	and	and	CCONJ
ejpam-5494	366	10	applications	application	NOUN
ejpam-5494	366	11	.	.	PUNCT
ejpam-5494	367	1	entropy	entropy	PROPN
ejpam-5494	367	2	,	,	PUNCT
ejpam-5494	367	3	15:5305–5323	15:5305–5323	NUM
ejpam-5494	367	4	,	,	PUNCT
ejpam-5494	367	5	2013	2013	NUM
ejpam-5494	367	6	.	.	PUNCT
ejpam-5494	368	1	[	[	X
ejpam-5494	368	2	12	12	NUM
ejpam-5494	368	3	]	]	PUNCT
ejpam-5494	368	4	v.	v.	CCONJ
ejpam-5494	368	5	s.	s.	PROPN
ejpam-5494	368	6	ertürk	ertürk	PROPN
ejpam-5494	368	7	and	and	CCONJ
ejpam-5494	368	8	s.	s.	PROPN
ejpam-5494	368	9	momani	momani	PROPN
ejpam-5494	368	10	.	.	PUNCT
ejpam-5494	369	1	solving	solve	VERB
ejpam-5494	369	2	systems	system	NOUN
ejpam-5494	369	3	of	of	ADP
ejpam-5494	369	4	fractional	fractional	ADJ
ejpam-5494	369	5	differential	differential	ADJ
ejpam-5494	369	6	equations	equation	NOUN
ejpam-5494	369	7	using	use	VERB
ejpam-5494	369	8	differential	differential	ADJ
ejpam-5494	369	9	transform	transform	NOUN
ejpam-5494	369	10	method	method	NOUN
ejpam-5494	369	11	.	.	PUNCT
ejpam-5494	370	1	journal	journal	NOUN
ejpam-5494	370	2	of	of	ADP
ejpam-5494	370	3	computational	computational	ADJ
ejpam-5494	370	4	and	and	CCONJ
ejpam-5494	370	5	applied	applied	ADJ
ejpam-5494	370	6	mathematics	mathematic	NOUN
ejpam-5494	370	7	,	,	PUNCT
ejpam-5494	370	8	215(1):142–151	215(1):142–151	NUM
ejpam-5494	370	9	,	,	PUNCT
ejpam-5494	370	10	2008	2008	NUM
ejpam-5494	370	11	.	.	PUNCT
ejpam-5494	371	1	[	[	X
ejpam-5494	371	2	13	13	NUM
ejpam-5494	371	3	]	]	PUNCT
ejpam-5494	371	4	a.	a.	PROPN
ejpam-5494	371	5	r.	r.	PROPN
ejpam-5494	371	6	hadhoud	hadhoud	PROPN
ejpam-5494	371	7	,	,	PUNCT
ejpam-5494	371	8	a.	a.	NOUN
ejpam-5494	371	9	a.	a.	NOUN
ejpam-5494	371	10	rageh	rageh	NOUN
ejpam-5494	371	11	,	,	PUNCT
ejpam-5494	371	12	and	and	CCONJ
ejpam-5494	371	13	t.	t.	NOUN
ejpam-5494	371	14	radwan	radwan	NOUN
ejpam-5494	371	15	.	.	PUNCT
ejpam-5494	372	1	employing	employ	VERB
ejpam-5494	372	2	the	the	DET
ejpam-5494	372	3	laplace	laplace	NOUN
ejpam-5494	372	4	residual	residual	ADJ
ejpam-5494	372	5	power	power	NOUN
ejpam-5494	372	6	series	series	PROPN
ejpam-5494	372	7	method	method	NOUN
ejpam-5494	372	8	to	to	PART
ejpam-5494	372	9	solve	solve	VERB
ejpam-5494	372	10	(	(	PUNCT
ejpam-5494	372	11	1	1	NUM
ejpam-5494	372	12	+	+	NOUN
ejpam-5494	372	13	1)and	1)and	NUM
ejpam-5494	372	14	(	(	PUNCT
ejpam-5494	372	15	2	2	NUM
ejpam-5494	372	16	+	+	NOUN
ejpam-5494	372	17	1)-dimensional	1)-dimensional	ADJ
ejpam-5494	372	18	time	time	NOUN
ejpam-5494	372	19	-	-	PUNCT
ejpam-5494	372	20	fractional	fractional	ADJ
ejpam-5494	372	21	nonlinear	nonlinear	ADJ
ejpam-5494	372	22	differential	differential	ADJ
ejpam-5494	372	23	equations	equation	NOUN
ejpam-5494	372	24	.	.	PUNCT
ejpam-5494	373	1	fractal	fractal	PROPN
ejpam-5494	373	2	and	and	CCONJ
ejpam-5494	373	3	fractional	fractional	ADJ
ejpam-5494	373	4	,	,	PUNCT
ejpam-5494	373	5	8(7	8(7	NUM
ejpam-5494	373	6	)	)	PUNCT
ejpam-5494	373	7	,	,	PUNCT
ejpam-5494	373	8	2024	2024	NUM
ejpam-5494	373	9	.	.	PUNCT
ejpam-5494	374	1	[	[	X
ejpam-5494	374	2	14	14	NUM
ejpam-5494	374	3	]	]	X
ejpam-5494	374	4	e.	e.	PROPN
ejpam-5494	374	5	hesameddini	hesameddini	PROPN
ejpam-5494	374	6	and	and	CCONJ
ejpam-5494	374	7	a.	a.	NOUN
ejpam-5494	374	8	rahimi	rahimi	NOUN
ejpam-5494	374	9	.	.	PUNCT
ejpam-5494	375	1	a	a	DET
ejpam-5494	375	2	novel	novel	ADJ
ejpam-5494	375	3	iterative	iterative	NOUN
ejpam-5494	375	4	method	method	NOUN
ejpam-5494	375	5	for	for	ADP
ejpam-5494	375	6	solving	solve	VERB
ejpam-5494	375	7	systems	system	NOUN
ejpam-5494	375	8	of	of	ADP
ejpam-5494	375	9	fractional	fractional	ADJ
ejpam-5494	375	10	differential	differential	ADJ
ejpam-5494	375	11	equations	equation	NOUN
ejpam-5494	375	12	.	.	PUNCT
ejpam-5494	376	1	journal	journal	PROPN
ejpam-5494	376	2	of	of	ADP
ejpam-5494	376	3	applied	apply	VERB
ejpam-5494	376	4	mathematics	mathematic	NOUN
ejpam-5494	376	5	,	,	PUNCT
ejpam-5494	376	6	2013(1	2013(1	NUM
ejpam-5494	376	7	)	)	PUNCT
ejpam-5494	376	8	,	,	PUNCT
ejpam-5494	376	9	2012	2012	NUM
ejpam-5494	376	10	.	.	PUNCT
ejpam-5494	377	1	[	[	X
ejpam-5494	377	2	15	15	NUM
ejpam-5494	377	3	]	]	X
ejpam-5494	377	4	h.	h.	PROPN
ejpam-5494	377	5	jafari	jafari	PROPN
ejpam-5494	377	6	and	and	CCONJ
ejpam-5494	377	7	v.	v.	ADP
ejpam-5494	377	8	daftardar	daftardar	NOUN
ejpam-5494	377	9	-	-	PUNCT
ejpam-5494	377	10	gejji	gejji	NOUN
ejpam-5494	377	11	.	.	PUNCT
ejpam-5494	378	1	solving	solve	VERB
ejpam-5494	378	2	a	a	DET
ejpam-5494	378	3	system	system	NOUN
ejpam-5494	378	4	of	of	ADP
ejpam-5494	378	5	nonlinear	nonlinear	ADJ
ejpam-5494	378	6	fractional	fractional	ADJ
ejpam-5494	378	7	differential	differential	NOUN
ejpam-5494	378	8	equations	equation	NOUN
ejpam-5494	378	9	using	use	VERB
ejpam-5494	378	10	adomian	adomian	NOUN
ejpam-5494	378	11	decomposition	decomposition	NOUN
ejpam-5494	378	12	.	.	PUNCT
ejpam-5494	379	1	journal	journal	NOUN
ejpam-5494	379	2	of	of	ADP
ejpam-5494	379	3	computational	computational	ADJ
ejpam-5494	379	4	and	and	CCONJ
ejpam-5494	379	5	applied	applied	ADJ
ejpam-5494	379	6	mathematics	mathematic	NOUN
ejpam-5494	379	7	,	,	PUNCT
ejpam-5494	379	8	196(2):644–651	196(2):644–651	NUM
ejpam-5494	379	9	,	,	PUNCT
ejpam-5494	379	10	2006	2006	NUM
ejpam-5494	379	11	.	.	PUNCT
ejpam-5494	380	1	[	[	X
ejpam-5494	380	2	16	16	NUM
ejpam-5494	380	3	]	]	X
ejpam-5494	380	4	h.	h.	PROPN
ejpam-5494	380	5	jafari	jafari	PROPN
ejpam-5494	380	6	and	and	CCONJ
ejpam-5494	380	7	s.	s.	PROPN
ejpam-5494	380	8	seifi	seifi	NOUN
ejpam-5494	380	9	.	.	PUNCT
ejpam-5494	381	1	solving	solve	VERB
ejpam-5494	381	2	a	a	DET
ejpam-5494	381	3	system	system	NOUN
ejpam-5494	381	4	of	of	ADP
ejpam-5494	381	5	nonlinear	nonlinear	ADJ
ejpam-5494	381	6	fractional	fractional	ADJ
ejpam-5494	381	7	partial	partial	ADJ
ejpam-5494	381	8	differential	differential	NOUN
ejpam-5494	381	9	equations	equation	NOUN
ejpam-5494	381	10	using	use	VERB
ejpam-5494	381	11	homotopy	homotopy	NOUN
ejpam-5494	381	12	analysis	analysis	NOUN
ejpam-5494	381	13	method	method	NOUN
ejpam-5494	381	14	.	.	PUNCT
ejpam-5494	382	1	communications	communication	NOUN
ejpam-5494	382	2	in	in	ADP
ejpam-5494	382	3	nonlinear	nonlinear	ADJ
ejpam-5494	382	4	science	science	NOUN
ejpam-5494	382	5	and	and	CCONJ
ejpam-5494	382	6	numerical	numerical	PROPN
ejpam-5494	382	7	simulation	simulation	PROPN
ejpam-5494	382	8	,	,	PUNCT
ejpam-5494	382	9	14(5):1962–1966	14(5):1962–1966	NUM
ejpam-5494	382	10	,	,	PUNCT
ejpam-5494	382	11	2009	2009	NUM
ejpam-5494	382	12	.	.	PUNCT
ejpam-5494	383	1	[	[	X
ejpam-5494	383	2	17	17	NUM
ejpam-5494	383	3	]	]	X
ejpam-5494	383	4	g.	g.	PROPN
ejpam-5494	383	5	mittag	mittag	ADJ
ejpam-5494	383	6	-	-	PUNCT
ejpam-5494	383	7	leffler	leffler	NOUN
ejpam-5494	383	8	.	.	PUNCT
ejpam-5494	384	1	“	"	PUNCT
ejpam-5494	384	2	sur	sur	PROPN
ejpam-5494	384	3	la	la	X
ejpam-5494	384	4	nouvelle	nouvelle	PROPN
ejpam-5494	384	5	fonction	fonction	PROPN
ejpam-5494	384	6	eα(x	eα(x	PROPN
ejpam-5494	384	7	)	)	PUNCT
ejpam-5494	384	8	”	"	PUNCT
ejpam-5494	384	9	.	.	PUNCT
ejpam-5494	384	10	comptes	compte	VERB
ejpam-5494	384	11	rendus	rendus	PROPN
ejpam-5494	384	12	de	de	PROPN
ejpam-5494	384	13	l’academie	l’academie	VERB
ejpam-5494	384	14	des	des	PROPN
ejpam-5494	384	15	sciences	sciences	PROPN
ejpam-5494	384	16	paris	paris	PROPN
ejpam-5494	384	17	,	,	PUNCT
ejpam-5494	384	18	137:554–558	137:554–558	NUM
ejpam-5494	384	19	,	,	PUNCT
ejpam-5494	384	20	1903	1903	NUM
ejpam-5494	384	21	.	.	PUNCT
ejpam-5494	385	1	[	[	X
ejpam-5494	385	2	18	18	NUM
ejpam-5494	385	3	]	]	PUNCT
ejpam-5494	385	4	i.	i.	NOUN
ejpam-5494	385	5	podlubny	podlubny	PROPN
ejpam-5494	385	6	.	.	PUNCT
ejpam-5494	386	1	fractional	fractional	ADJ
ejpam-5494	386	2	differential	differential	ADJ
ejpam-5494	386	3	equations	equation	NOUN
ejpam-5494	386	4	.	.	PUNCT
ejpam-5494	387	1	academic	academic	ADJ
ejpam-5494	387	2	press	press	NOUN
ejpam-5494	387	3	,	,	PUNCT
ejpam-5494	387	4	new	new	PROPN
ejpam-5494	387	5	york	york	PROPN
ejpam-5494	387	6	,	,	PUNCT
ejpam-5494	387	7	1999	1999	NUM
ejpam-5494	387	8	.	.	PUNCT
ejpam-5494	388	1	[	[	X
ejpam-5494	388	2	19	19	NUM
ejpam-5494	388	3	]	]	SYM
ejpam-5494	388	4	s.n.t	s.n.t	NOUN
ejpam-5494	388	5	.	.	PUNCT
ejpam-5494	388	6	polat	polat	NOUN
ejpam-5494	388	7	and	and	CCONJ
ejpam-5494	388	8	a.t	a.t	PROPN
ejpam-5494	388	9	.	.	PROPN
ejpam-5494	388	10	dincel	dincel	PROPN
ejpam-5494	388	11	.	.	PUNCT
ejpam-5494	389	1	solution	solution	NOUN
ejpam-5494	389	2	method	method	NOUN
ejpam-5494	389	3	for	for	ADP
ejpam-5494	389	4	systems	system	NOUN
ejpam-5494	389	5	of	of	ADP
ejpam-5494	389	6	nonlinear	nonlinear	ADJ
ejpam-5494	389	7	fractional	fractional	ADJ
ejpam-5494	389	8	differential	differential	NOUN
ejpam-5494	389	9	equations	equation	NOUN
ejpam-5494	389	10	using	use	VERB
ejpam-5494	389	11	third	third	ADJ
ejpam-5494	389	12	kind	kind	ADJ
ejpam-5494	389	13	chebyshev	chebyshev	NOUN
ejpam-5494	389	14	wavelets	wavelet	NOUN
ejpam-5494	389	15	.	.	PUNCT
ejpam-5494	390	1	axioms	axiom	NOUN
ejpam-5494	390	2	,	,	PUNCT
ejpam-5494	390	3	12(546):12	12(546):12	NUM
ejpam-5494	390	4	pages	page	NOUN
ejpam-5494	390	5	,	,	PUNCT
ejpam-5494	390	6	2023	2023	NUM
ejpam-5494	390	7	.	.	PUNCT
ejpam-5494	391	1	[	[	X
ejpam-5494	391	2	20	20	NUM
ejpam-5494	391	3	]	]	PUNCT
ejpam-5494	391	4	p.	p.	NOUN
ejpam-5494	391	5	pue	pue	NOUN
ejpam-5494	391	6	-	-	PUNCT
ejpam-5494	391	7	on	on	ADP
ejpam-5494	391	8	.	.	PUNCT
ejpam-5494	392	1	the	the	DET
ejpam-5494	392	2	modified	modify	VERB
ejpam-5494	392	3	sadik	sadik	PROPN
ejpam-5494	392	4	decomposition	decomposition	NOUN
ejpam-5494	392	5	method	method	NOUN
ejpam-5494	392	6	to	to	PART
ejpam-5494	392	7	solve	solve	VERB
ejpam-5494	392	8	a	a	DET
ejpam-5494	392	9	system	system	NOUN
ejpam-5494	392	10	of	of	ADP
ejpam-5494	392	11	nonlinear	nonlinear	ADJ
ejpam-5494	392	12	fractional	fractional	PROPN
ejpam-5494	392	13	volterra	volterra	PROPN
ejpam-5494	392	14	integrodifferential	integrodifferential	ADJ
ejpam-5494	392	15	equations	equation	NOUN
ejpam-5494	392	16	of	of	ADP
ejpam-5494	392	17	convolution	convolution	NOUN
ejpam-5494	392	18	type	type	NOUN
ejpam-5494	392	19	.	.	PUNCT
ejpam-5494	393	1	wseas	wseas	NOUN
ejpam-5494	393	2	transactions	transaction	NOUN
ejpam-5494	393	3	on	on	ADP
ejpam-5494	393	4	mathematics	mathematic	NOUN
ejpam-5494	393	5	,	,	PUNCT
ejpam-5494	393	6	20:335–343	20:335–343	PROPN
ejpam-5494	393	7	,	,	PUNCT
ejpam-5494	393	8	2021	2021	NUM
ejpam-5494	393	9	.	.	PUNCT
ejpam-5494	394	1	references	reference	NOUN
ejpam-5494	394	2	3846	3846	NUM
ejpam-5494	394	3	[	[	X
ejpam-5494	394	4	21	21	NUM
ejpam-5494	394	5	]	]	X
ejpam-5494	394	6	p.	p.	NOUN
ejpam-5494	394	7	pue	pue	NOUN
ejpam-5494	394	8	-	-	PUNCT
ejpam-5494	394	9	on	on	ADP
ejpam-5494	394	10	.	.	PUNCT
ejpam-5494	395	1	the	the	DET
ejpam-5494	395	2	exact	exact	ADJ
ejpam-5494	395	3	solutions	solution	NOUN
ejpam-5494	395	4	of	of	ADP
ejpam-5494	395	5	the	the	DET
ejpam-5494	395	6	space	space	NOUN
ejpam-5494	395	7	and	and	CCONJ
ejpam-5494	395	8	time	time	NOUN
ejpam-5494	395	9	fractional	fractional	PROPN
ejpam-5494	395	10	telegraph	telegraph	NOUN
ejpam-5494	395	11	equations	equation	NOUN
ejpam-5494	395	12	by	by	ADP
ejpam-5494	395	13	the	the	DET
ejpam-5494	395	14	double	double	ADJ
ejpam-5494	395	15	sadik	sadik	PROPN
ejpam-5494	395	16	transform	transform	NOUN
ejpam-5494	395	17	method	method	NOUN
ejpam-5494	395	18	.	.	PUNCT
ejpam-5494	396	1	mathematics	mathematic	NOUN
ejpam-5494	396	2	and	and	CCONJ
ejpam-5494	396	3	statistics	statistic	NOUN
ejpam-5494	396	4	,	,	PUNCT
ejpam-5494	396	5	10(5):995–1004	10(5):995–1004	NUM
ejpam-5494	396	6	,	,	PUNCT
ejpam-5494	396	7	2022	2022	NUM
ejpam-5494	396	8	.	.	PUNCT
ejpam-5494	397	1	[	[	X
ejpam-5494	397	2	22	22	NUM
ejpam-5494	397	3	]	]	X
ejpam-5494	397	4	p.	p.	NOUN
ejpam-5494	397	5	pue	pue	NOUN
ejpam-5494	397	6	-	-	PUNCT
ejpam-5494	397	7	on	on	ADP
ejpam-5494	397	8	.	.	PUNCT
ejpam-5494	398	1	exploring	explore	VERB
ejpam-5494	398	2	the	the	DET
ejpam-5494	398	3	remarkable	remarkable	ADJ
ejpam-5494	398	4	properties	property	NOUN
ejpam-5494	398	5	of	of	ADP
ejpam-5494	398	6	the	the	DET
ejpam-5494	398	7	double	double	ADJ
ejpam-5494	398	8	sadik	sadik	PROPN
ejpam-5494	398	9	transform	transform	NOUN
ejpam-5494	398	10	and	and	CCONJ
ejpam-5494	398	11	its	its	PRON
ejpam-5494	398	12	applications	application	NOUN
ejpam-5494	398	13	to	to	ADP
ejpam-5494	398	14	fractional	fractional	VERB
ejpam-5494	398	15	caputo	caputo	PROPN
ejpam-5494	398	16	partial	partial	ADJ
ejpam-5494	398	17	differential	differential	NOUN
ejpam-5494	398	18	equations	equation	NOUN
ejpam-5494	398	19	.	.	PUNCT
ejpam-5494	399	1	international	international	ADJ
ejpam-5494	399	2	journal	journal	NOUN
ejpam-5494	399	3	of	of	ADP
ejpam-5494	399	4	analysis	analysis	NOUN
ejpam-5494	399	5	and	and	CCONJ
ejpam-5494	399	6	applications	application	NOUN
ejpam-5494	399	7	.	.	PUNCT
ejpam-5494	399	8	,	,	PUNCT
ejpam-5494	399	9	21(118	21(118	NOUN
ejpam-5494	399	10	)	)	PUNCT
ejpam-5494	399	11	,	,	PUNCT
ejpam-5494	399	12	2023	2023	NUM
ejpam-5494	399	13	.	.	PUNCT
ejpam-5494	400	1	[	[	X
ejpam-5494	400	2	23	23	NUM
ejpam-5494	400	3	]	]	PUNCT
ejpam-5494	400	4	a.	a.	NOUN
ejpam-5494	400	5	qazza	qazza	PROPN
ejpam-5494	400	6	,	,	PUNCT
ejpam-5494	400	7	a.	a.	NOUN
ejpam-5494	400	8	burqan	burqan	PROPN
ejpam-5494	400	9	,	,	PUNCT
ejpam-5494	400	10	and	and	CCONJ
ejpam-5494	400	11	r.	r.	PROPN
ejpam-5494	400	12	saadeh	saadeh	PROPN
ejpam-5494	400	13	.	.	PUNCT
ejpam-5494	401	1	application	application	NOUN
ejpam-5494	401	2	of	of	ADP
ejpam-5494	401	3	ara	ara	NOUN
ejpam-5494	401	4	-	-	PUNCT
ejpam-5494	401	5	residual	residual	ADJ
ejpam-5494	401	6	power	power	NOUN
ejpam-5494	401	7	series	series	NOUN
ejpam-5494	401	8	method	method	NOUN
ejpam-5494	401	9	in	in	ADP
ejpam-5494	401	10	solving	solve	VERB
ejpam-5494	401	11	systems	system	NOUN
ejpam-5494	401	12	of	of	ADP
ejpam-5494	401	13	fractional	fractional	ADJ
ejpam-5494	401	14	differential	differential	ADJ
ejpam-5494	401	15	equations	equation	NOUN
ejpam-5494	401	16	.	.	PUNCT
ejpam-5494	402	1	mathematical	mathematical	ADJ
ejpam-5494	402	2	problems	problem	NOUN
ejpam-5494	402	3	in	in	ADP
ejpam-5494	402	4	engineering	engineering	NOUN
ejpam-5494	402	5	,	,	PUNCT
ejpam-5494	402	6	2022(1	2022(1	NUM
ejpam-5494	402	7	)	)	PUNCT
ejpam-5494	402	8	,	,	PUNCT
ejpam-5494	402	9	2021	2021	NUM
ejpam-5494	402	10	.	.	PUNCT
ejpam-5494	403	1	[	[	X
ejpam-5494	403	2	24	24	NUM
ejpam-5494	403	3	]	]	PUNCT
ejpam-5494	403	4	a.	a.	NOUN
ejpam-5494	403	5	raheem	raheem	NOUN
ejpam-5494	403	6	and	and	CCONJ
ejpam-5494	403	7	a.	a.	PROPN
ejpam-5494	403	8	afreen	afreen	PROPN
ejpam-5494	403	9	.	.	PUNCT
ejpam-5494	404	1	study	study	NOUN
ejpam-5494	404	2	of	of	ADP
ejpam-5494	404	3	a	a	DET
ejpam-5494	404	4	nonlinear	nonlinear	ADJ
ejpam-5494	404	5	system	system	NOUN
ejpam-5494	404	6	of	of	ADP
ejpam-5494	404	7	fractional	fractional	ADJ
ejpam-5494	404	8	differential	differential	ADJ
ejpam-5494	404	9	equations	equation	NOUN
ejpam-5494	404	10	with	with	ADP
ejpam-5494	404	11	deviated	deviate	VERB
ejpam-5494	404	12	arguments	argument	NOUN
ejpam-5494	404	13	via	via	ADP
ejpam-5494	404	14	adomian	adomian	ADJ
ejpam-5494	404	15	decomposition	decomposition	NOUN
ejpam-5494	404	16	method	method	NOUN
ejpam-5494	404	17	.	.	PUNCT
ejpam-5494	405	1	international	international	ADJ
ejpam-5494	405	2	journal	journal	PROPN
ejpam-5494	405	3	of	of	ADP
ejpam-5494	405	4	applied	applied	ADJ
ejpam-5494	405	5	and	and	CCONJ
ejpam-5494	405	6	computational	computational	ADJ
ejpam-5494	405	7	mathematics	mathematic	NOUN
ejpam-5494	405	8	,	,	PUNCT
ejpam-5494	405	9	8(269):17	8(269):17	NUM
ejpam-5494	405	10	pages	page	NOUN
ejpam-5494	405	11	,	,	PUNCT
ejpam-5494	405	12	2022	2022	NUM
ejpam-5494	405	13	.	.	PUNCT
ejpam-5494	406	1	[	[	X
ejpam-5494	406	2	25	25	NUM
ejpam-5494	406	3	]	]	PUNCT
ejpam-5494	406	4	s.	s.	PROPN
ejpam-5494	406	5	s.	s.	PROPN
ejpam-5494	406	6	redhwan	redhwan	PROPN
ejpam-5494	406	7	,	,	PUNCT
ejpam-5494	406	8	s.	s.	PROPN
ejpam-5494	406	9	l.	l.	PROPN
ejpam-5494	406	10	shaikh	shaikh	PROPN
ejpam-5494	406	11	,	,	PUNCT
ejpam-5494	406	12	and	and	CCONJ
ejpam-5494	406	13	m.	m.	NOUN
ejpam-5494	406	14	s.	s.	PROPN
ejpam-5494	406	15	abdo	abdo	PROPN
ejpam-5494	406	16	.	.	PUNCT
ejpam-5494	407	1	some	some	DET
ejpam-5494	407	2	properties	property	NOUN
ejpam-5494	407	3	of	of	ADP
ejpam-5494	407	4	sadik	sadik	PROPN
ejpam-5494	407	5	transform	transform	NOUN
ejpam-5494	407	6	and	and	CCONJ
ejpam-5494	407	7	its	its	PRON
ejpam-5494	407	8	applications	application	NOUN
ejpam-5494	407	9	of	of	ADP
ejpam-5494	407	10	fractional	fractional	ADJ
ejpam-5494	407	11	-	-	PUNCT
ejpam-5494	407	12	order	order	NOUN
ejpam-5494	407	13	dynamical	dynamical	ADJ
ejpam-5494	407	14	systems	system	NOUN
ejpam-5494	407	15	in	in	ADP
ejpam-5494	407	16	control	control	NOUN
ejpam-5494	407	17	theory	theory	NOUN
ejpam-5494	407	18	.	.	PUNCT
ejpam-5494	408	1	advances	advance	NOUN
ejpam-5494	408	2	in	in	ADP
ejpam-5494	408	3	the	the	DET
ejpam-5494	408	4	theory	theory	NOUN
ejpam-5494	408	5	of	of	ADP
ejpam-5494	408	6	nonlinear	nonlinear	ADJ
ejpam-5494	408	7	analysis	analysis	NOUN
ejpam-5494	408	8	and	and	CCONJ
ejpam-5494	408	9	its	its	PRON
ejpam-5494	408	10	applications	application	NOUN
ejpam-5494	408	11	,	,	PUNCT
ejpam-5494	408	12	4:51–66	4:51–66	NUM
ejpam-5494	408	13	,	,	PUNCT
ejpam-5494	408	14	2020	2020	NUM
ejpam-5494	408	15	.	.	PUNCT
ejpam-5494	409	1	[	[	X
ejpam-5494	409	2	26	26	NUM
ejpam-5494	409	3	]	]	PUNCT
ejpam-5494	409	4	s.	s.	PROPN
ejpam-5494	409	5	s.	s.	PROPN
ejpam-5494	409	6	redhwan	redhwan	PROPN
ejpam-5494	409	7	,	,	PUNCT
ejpam-5494	409	8	s.	s.	PROPN
ejpam-5494	409	9	l.	l.	PROPN
ejpam-5494	409	10	shaikh	shaikh	PROPN
ejpam-5494	409	11	,	,	PUNCT
ejpam-5494	409	12	m.	m.	NOUN
ejpam-5494	409	13	s.	s.	PROPN
ejpam-5494	409	14	abdo	abdo	PROPN
ejpam-5494	409	15	,	,	PUNCT
ejpam-5494	409	16	and	and	CCONJ
ejpam-5494	409	17	s.	s.	PROPN
ejpam-5494	409	18	y.	y.	PROPN
ejpam-5494	409	19	al	al	PROPN
ejpam-5494	409	20	-	-	PUNCT
ejpam-5494	409	21	mayyahi	mayyahi	PROPN
ejpam-5494	409	22	.	.	PUNCT
ejpam-5494	410	1	sadik	sadik	PROPN
ejpam-5494	410	2	transform	transform	VERB
ejpam-5494	410	3	and	and	CCONJ
ejpam-5494	410	4	some	some	DET
ejpam-5494	410	5	result	result	NOUN
ejpam-5494	410	6	in	in	ADP
ejpam-5494	410	7	fractional	fractional	ADJ
ejpam-5494	410	8	calculus	calculus	NOUN
ejpam-5494	410	9	.	.	PUNCT
ejpam-5494	411	1	malaya	malaya	PROPN
ejpam-5494	411	2	journal	journal	PROPN
ejpam-5494	411	3	of	of	ADP
ejpam-5494	411	4	matematik	matematik	PROPN
ejpam-5494	411	5	,	,	PUNCT
ejpam-5494	411	6	8(2):536–543	8(2):536–543	NUM
ejpam-5494	411	7	,	,	PUNCT
ejpam-5494	411	8	2020	2020	NUM
ejpam-5494	411	9	.	.	PUNCT
ejpam-5494	412	1	[	[	X
ejpam-5494	412	2	27	27	NUM
ejpam-5494	412	3	]	]	PUNCT
ejpam-5494	412	4	s.	s.	PROPN
ejpam-5494	412	5	l.	l.	PROPN
ejpam-5494	412	6	shaikh	shaikh	PROPN
ejpam-5494	412	7	.	.	PUNCT
ejpam-5494	413	1	introducing	introduce	VERB
ejpam-5494	413	2	a	a	DET
ejpam-5494	413	3	new	new	ADJ
ejpam-5494	413	4	integral	integral	ADJ
ejpam-5494	413	5	transform	transform	NOUN
ejpam-5494	413	6	:	:	PUNCT
ejpam-5494	413	7	sadik	sadik	ADJ
ejpam-5494	413	8	transform	transform	NOUN
ejpam-5494	413	9	.	.	PUNCT
ejpam-5494	414	1	american	american	PROPN
ejpam-5494	414	2	international	international	PROPN
ejpam-5494	414	3	journal	journal	PROPN
ejpam-5494	414	4	of	of	ADP
ejpam-5494	414	5	research	research	NOUN
ejpam-5494	414	6	in	in	ADP
ejpam-5494	414	7	science	science	NOUN
ejpam-5494	414	8	,	,	PUNCT
ejpam-5494	414	9	technology	technology	NOUN
ejpam-5494	414	10	,	,	PUNCT
ejpam-5494	414	11	engineering	engineering	NOUN
ejpam-5494	414	12	&	&	CCONJ
ejpam-5494	414	13	mathematics	mathematic	NOUN
ejpam-5494	414	14	,	,	PUNCT
ejpam-5494	414	15	22:100–102	22:100–102	NUM
ejpam-5494	414	16	,	,	PUNCT
ejpam-5494	414	17	2018	2018	NUM
ejpam-5494	414	18	.	.	PUNCT
ejpam-5494	415	1	[	[	X
ejpam-5494	415	2	28	28	NUM
ejpam-5494	415	3	]	]	X
ejpam-5494	415	4	k.	k.	PROPN
ejpam-5494	415	5	yuxiao	yuxiao	PROPN
ejpam-5494	415	6	m.	m.	PROPN
ejpam-5494	415	7	shuhua	shuhua	PROPN
ejpam-5494	415	8	z.	z.	PROPN
ejpam-5494	415	9	yonghong	yonghong	PROPN
ejpam-5494	415	10	.	.	PUNCT
ejpam-5494	416	1	variable	variable	ADJ
ejpam-5494	416	2	order	order	NOUN
ejpam-5494	416	3	fractional	fractional	ADJ
ejpam-5494	416	4	grey	grey	NOUN
ejpam-5494	416	5	model	model	NOUN
ejpam-5494	416	6	and	and	CCONJ
ejpam-5494	416	7	its	its	PRON
ejpam-5494	416	8	application	application	NOUN
ejpam-5494	416	9	.	.	PUNCT
ejpam-5494	417	1	applied	apply	VERB
ejpam-5494	417	2	mathematical	mathematical	ADJ
ejpam-5494	417	3	modelling	modelling	NOUN
ejpam-5494	417	4	,	,	PUNCT
ejpam-5494	417	5	97:619–635	97:619–635	PROPN
ejpam-5494	417	6	,	,	PUNCT
ejpam-5494	417	7	2021	2021	NUM
ejpam-5494	417	8	.	.	PUNCT
ejpam-5494	418	1	[	[	X
ejpam-5494	418	2	29	29	NUM
ejpam-5494	418	3	]	]	PUNCT
ejpam-5494	418	4	j.	j.	PROPN
ejpam-5494	418	5	zhang	zhang	PROPN
ejpam-5494	418	6	,	,	PUNCT
ejpam-5494	418	7	x.	x.	PROPN
ejpam-5494	418	8	chen	chen	PROPN
ejpam-5494	418	9	,	,	PUNCT
ejpam-5494	418	10	l.	l.	PROPN
ejpam-5494	418	11	li	li	PROPN
ejpam-5494	418	12	,	,	PUNCT
ejpam-5494	418	13	and	and	CCONJ
ejpam-5494	418	14	c.	c.	PROPN
ejpam-5494	418	15	zhou	zhou	PROPN
ejpam-5494	418	16	.	.	PUNCT
ejpam-5494	419	1	elzaki	elzaki	PROPN
ejpam-5494	419	2	transform	transform	VERB
ejpam-5494	419	3	residual	residual	ADJ
ejpam-5494	419	4	power	power	NOUN
ejpam-5494	419	5	series	series	NOUN
ejpam-5494	419	6	method	method	NOUN
ejpam-5494	419	7	for	for	ADP
ejpam-5494	419	8	the	the	DET
ejpam-5494	419	9	fractional	fractional	ADJ
ejpam-5494	419	10	population	population	NOUN
ejpam-5494	419	11	diffusion	diffusion	NOUN
ejpam-5494	419	12	equations	equation	NOUN
ejpam-5494	419	13	.	.	PUNCT
ejpam-5494	420	1	engineering	engineering	NOUN
ejpam-5494	420	2	letters	letter	NOUN
ejpam-5494	420	3	,	,	PUNCT
ejpam-5494	420	4	29(4):12	29(4):12	NUM
ejpam-5494	420	5	pages	page	NOUN
ejpam-5494	420	6	,	,	PUNCT
ejpam-5494	420	7	2021	2021	NUM
ejpam-5494	420	8	.	.	PUNCT
ejpam-5494	421	1	[	[	X
ejpam-5494	421	2	30	30	NUM
ejpam-5494	421	3	]	]	X
ejpam-5494	421	4	e.	e.	PROPN
ejpam-5494	421	5	ziada	ziada	PROPN
ejpam-5494	421	6	.	.	PUNCT
ejpam-5494	422	1	analytical	analytical	ADJ
ejpam-5494	422	2	solution	solution	NOUN
ejpam-5494	422	3	of	of	ADP
ejpam-5494	422	4	nonlinear	nonlinear	ADJ
ejpam-5494	422	5	system	system	NOUN
ejpam-5494	422	6	of	of	ADP
ejpam-5494	422	7	fractional	fractional	ADJ
ejpam-5494	422	8	differential	differential	ADJ
ejpam-5494	422	9	equations	equation	NOUN
ejpam-5494	422	10	.	.	PUNCT
ejpam-5494	423	1	journal	journal	PROPN
ejpam-5494	423	2	of	of	ADP
ejpam-5494	423	3	applied	apply	VERB
ejpam-5494	423	4	mathematics	mathematic	NOUN
ejpam-5494	423	5	and	and	CCONJ
ejpam-5494	423	6	physics	physics	NOUN
ejpam-5494	423	7	,	,	PUNCT
ejpam-5494	423	8	9(10):2544–2557	9(10):2544–2557	NUM
ejpam-5494	423	9	,	,	PUNCT
ejpam-5494	423	10	2021	2021	NUM
ejpam-5494	423	11	.	.	PUNCT